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REFERENCE MANUAL OF SSS - Simulation Subroutine Set. Version 1.00 Copyright (C) M. A. Pollatschek 1990. All rights reserved. ╔════════════╗ ║ CONTENTS ║ ╚════════════╝ Page HOW TO BENEFIT FROM THIS DOCUMENTATION.. ... ... ... 2 ALPHABETIC LIST OF ROUTINES... ... ... ... ... ... 2 TERMINOLOGY ... ... ... ... ... ... ... ... ... 2 SIMULATION ROUTINE.. ... ... ... ... ... ... ... 4 ERROR MASSAGES. ... ... ... ... ... ... ... ... 5 CLARIFICATION OF ENTRIES IN DESCRIPTION. ... ... ... 6 NOTES FOR EXAMPLES.. ... ... ... ... ... ... ... 6 A(n), IDE(), SETA(n,v) SETIDE(i)... ... ... ... ... 7 AIC(r,n), IDIC(r), NEIC(r), TIC(r). ... ... ... ... 8 AIQ(m,r,n), IDIQ(m,r), PRIQ(m,r)... ... ... ... ... 9 BE(W,U)... ... ... ... ... ... ... ... ... ...10 BI(N,P), NP(M). ... ... ... ... ... ... ... ...10 CD(X,V,N), DP(V,N).. ... ... ... ... ... ... ...11 CLEARQ(m), QAVG(m), QMAX(m), QMIN(m), QNUM(m), QSTD(m).12 CLEARS(j), TALLY(j,v) ... ... ... ... ... ... ...13 CREATE(g,i) ... ... ... ... ... ... ... ... ...14 DISPOS().. ... ... ... ... ... ... ... ... ...15 ER(M,K), EX(M), GA(M,K) WE(M,U)... ... ... ... ...15 INIQUE(q,b,s).. ... ... ... ... ... ... ... ...16 INISTA(j,h,k,l,f,w). ... ... ... ... ... ... ...16 NC(), NQ(m) ... ... ... ... ... ... ... ... ...18 NCEN(), NEXTEV() ... ... ... ... ... ... ... ...19 QDC(m), SETQDC(m,d). ... ... ... ... ... ... ...20 QUEUE(m,p) ... ... ... ... ... ... ... ... ...21 RA(), RL(M,S), RN(M,S), TR(I,B,C), UN(I,C)... ... ...22 REMVFC(r), REMVFQ(m,r)... ... ... ... ... ... ...23 SAVG(j), SMAX(j), SMIN(j), SNUM(j), SSTD(j).. ... ...24 SCHED(g,e,i)... ... ... ... ... ... ... ... ...25 SETANT(y), SETSEE(x) ... ... ... ... ... ... ...26 SETDEB(o), SHOWQ(m). ... ... ... ... ... ... ...27 SETT(g), T()... ... ... ... ... ... ... ... ...28 SIMEND(g). ... ... ... ... ... ... ... ... ...29 SIMERR().. ... ... ... ... ... ... ... ... ...30 SUMRY(u).. ... ... ... ... ... ... ... ... ...31 SSS Reference Page 2 ╔══════════════════════════════════════════╗ ║ HOW TO BENEFIT FROM THIS DOCUMENTATION ║ ╚══════════════════════════════════════════╝ Use a lister/editor's search facility to find out the meaning of terms. Each term is explained somewhere. Examine also the examples in files EX_*.*. Printed user guide with tutorials and/or source code is available. Write to: M. A. Pollatschek, Management, Technion, Haifa 32000 ISRAEL. ╔════════════════════════════════╗ ║ ALPHABETIC LIST OF ROUTINES ║ ║ and where they are described ║ ╚════════════════════════════════╝ for look for look for look for look routine under routine under routine under routine under A.......A IDIC....AIC QNUM....CLEARQ SETSEE..SETANT AIC.....AIC IDIQ....AIQ QSTD....CLEARQ SETT....SETT AIQ.....AIQ INIQUE..INIQUE QUEUE...QUEUE SHOWQ...SETDEB BE......BE INISTA..INISTA RA......RA SIMEND..SIMEND BI......BI NC......NC REMVFQ..REMVFQ SIMERR..SIMERR CD......CD NCEN....NCEN REMVFQ..REMVFQ SMAX....SAVG CLEARQ..CLEARQ NEIC....AIC RL......RA SMIN....SAVG CLEARS..CLEARS NEXTEV..NCEN RN......RA SNUM....SAVG CREATE..CREATE NP......BI SAVG....SAVG SSTD....SAVG DISPOS..DISPOS NQ......NC SCHED...SCHED SUMRY...SUMRY DP......CD PRIQ....AIQ SETA....A T.......SETT ER......ER QAVG....CLEARQ SETANT..SETANT TALLY...CLEARS EX......ER QDC.....QDC SETDEB..SETDEB TIC.....AIC GA......ER QMAX....CLEARQ SETIDE..A TR......RA IDE.....A QMIN....CLEARQ SETQDC..QDC UN......RA WE......ER ╔═══════════════╗ ║ TERMINOLOGY ║ ╚═══════════════╝ attribute: is a numerical characteristic of the entities, e.g. size, color code in a floating point number. Attributes may differ among entities. They are updated/initiated for current entity to v by SETA(v). They can be accessed by A(n), AIC(r,n), AIQ(m,r,n). calendar: a list of scheduled or created, entities, that is entities whose events occure at some simulted time in the future. The calendar is created by calling INIQUE(q,b,s). Entities are put on the calendar by CREATE(g,i) or SCHED(g,e,i). Entities are removed from the calendar by NEXTEV() or REMVFC(r). SSS Reference Page 3 current entity: the entity under present treatment. There must be at most one such entity at each time. Its number at any time is given by NCEN(). An entity becomes current after calling one of: NEXTEV(), REMVFC(r), REMVFQ(m,r) and stops being current after calling one of: DISPOS(), QUEUE(m,p), SCHED(g,e,i). discipline: the ordering of entities in a queue, may be one of: FIFO=first in first out, LIFO=first in last out, SVF=smallest value first, BVF=biggest value first. entity: the basic constituent of simulation which undergoes a few processes in time like a customer, a part, a pellet, etc. event: an occurrence of a specific operation at a certain time, like arrival, end of servicing, etc. id, identity: is used to differentiate between various kinds of entities, e.g. parts, pellets and transporters on a factory floor as integers. They are set to i by CREATE(g,i), SCHED(g,e,i), SETIDE(i). priority: a number which determines the rank of an entity in a queue having a BVF or SVF discipline - the entities are sorted by their priorities. returned value: the value returned by a (non void) function. simulated time: time that the simulator's clock shows, not related to real time or computation time. stochastic process: is a variable which changes at some points of time and we are interested in its time average rather than its simple average. An example is inventory: if first three days we have 5 units, and the fourth day only 3 then the time average is (5*3 + 3*1)/4 = 4.5 and while the simple average is (5 + 3)/2 = 4. subroutine: a procedure or function. time persistent statistic: a statistic about a stochastic process. SSS Reference Page 4 ╔══════════════════════╗ ║ SIMULATION ROUTINE ║ ╚══════════════════════╝ The simulation program has two parts: [1] setup - contains calls to INIQUE, INISTA, at least one call to CREATE and other initializations; [2] event loop - what to do when an event happens. A skeleton event loop looks as follows: ╔══════════════╦════════════╦═════════════════╦═════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠══════════════╬════════════╬═════════════════╬═════════════╣ ║do ║do { ║9 e=NEXTEV() ║repeat ║ ║e=NEXTEV ║e=NEXTEV() ║ if(e.gt.0) then║e:=NEXTEV ║ ║if e>0 then ║if (e) ║ goto(1,2,...)e ║if e>0 then ║ ║select case e ║switch(e) { ║1 continue ║begin ║ ║case 1 ║case 1: ║C new entity ║case e of ║ ║ 'new entity ║/*new entity║C arrival ║1:{new entity║ ║ 'arrival ║ arrival */║ goto 9 ║ arrival} ║ ║case 2 ║case 2: ║2 continue ║2: ║ ║ 'etc ║ /* etc */ ║C etc ║ {etc} ║ ║end select ║} ║ goto 9 ║end {case}; ║ ║end if ║} ║ ... ║end {if}; ║ ║loop while e>0║while(e); ║ endif ║until e=0; ║ ╚══════════════╩════════════╩═════════════════╩═════════════╝ (In FORTRAN the first column here is actually the 5th and the C's must be actually in the 1st column.) The cases 1, 2, etc (in FORTRAN the goto labels) are the event codes. The significance of e is: 0: either the calendar is empty or end of simulation, placed on calendar by SIMEND(g). 1: a new entity's arrival caused by calling CREATE(g,i) at some earlier simulated time. Other values (greater than 1) are non-arrival events scheduled by SCHED(g,e,i) like end of service etc. SSS Reference Page 5 The codes following the cases are the things to perform at each event (like entering or inspecting a queue, starting or finishing an activity, etc). We suggest the following list covering most of the cases: ╔══════════╦════════════════════════════════════════════════════╗ ║Symbol(=e)║ Things to do when this event becomes current: ║ ╠══════════╬════════════════════════════════════════════════════╣ ║ARRIVL(=1)║SCHEDuling next ARRIVaL, determination of Attributes║ ║ ║and IDEntity of current entity as well as its first ║ ║ ║activity ║ ║ ║ ║ ║NEXTAC(=2)║preparing NEXT ACtivity: whether it can start or ║ ║ ║not, choosing of queues/servers if necessary ║ ║ ║ ║ ║STARTA(=3)║STARTing Activity: SCHEDuling its end ║ ║ ║ ║ ║ENDACT(=4)║ENDing ACTivity: determining what a server, who is ║ ║ ║freed from current entity, and the current entity ║ ║ ║should do next ║ ║ ║ ║ ║MATCH (=5)║MATCHing entities ║ ╚══════════╩════════════════════════════════════════════════════╝ The simulation is in a fact a proper interaction with the calendar. The important routines are: CREATE(g,i), NEXTEV() and SCHED(g,e,i). The calendar is fed with new entities by CREATE(g,i) and depleted by NEXTEV(). SCHED(g,e,i) sends the current entity to its next event e after a delay of g units time from present simulated time. It acts as a kind of delayed "goto". ╔══════════════════╗ ║ ERROR MASSAGES ║ ╚══════════════════╝ Most errors are explained under the routines that may raise them. There are two errors not covered under the routines: * There is no more space in memory or too many entities. Very unlikely, but may happen inside QuickBasic or QuickC environments. You may do one ore more of the following: [1] create less entities (if possible) [2] remove memory resident programs [3] add more physical memory (if possible) [4] in QuickBasic: consult end of SSSB.H for advice [5] in QuickBasic or QuickC: make compilation form CQ or QCL SSS Reference Page 6 * There is a mathematical error (like division by 0 or square root from a negative number) inside a random number generator. Very unlikely, but if happens, please report the exact circumstances to the author. You can circumvent it by using an alternative strategy of generation (via CD, for example). See error codes and massages on page 30 as well as ways to control them. ╔══════════════════════════════════════════╗ ║ CLARIFICATION OF ENTRIES IN DESCRIPTION ║ ╚══════════════════════════════════════════╝ Error: refers situations (invalid parameters or presence/absence of current entity) which give rise to errors Floating point number: double or real or real*8, see .H files Forbidden predecessor: a routine which must not be called prior to the routine under consideration unless one of the mandatory predecessors is called between them. For example, you cannot remove an entity from a queue (call REMVFQ(m,r)) unless there exists no current entity. But a current entity comes to existence as a result of calling NEXTEV(). NEXTEV() is therefore forbidden unless that entity is disposed (by calling DISPOS()) before calling REMVFQ(m,r). DISPOS() is mandatory here. Integer: 2 byte integer Notes: aspects concerning pecularities of languages Remarks: aspects concerning SSS or simulation or use ╔══════════════════════╗ ║ NOTES FOR EXAMPLES ║ ╚══════════════════════╝ In BASIC examples: _ signifies that following line is actually a continuation of present line; sometimes closing quote (") is missing for lack of space. In FORTRAN examples: first FORTRAN column is actually 5th column of code; sometimes closing quote (') is missing for lack of space. SSS Reference Page 7 ╔════════════════════════════════════╗ ║ A(n), IDE(), SETA(n,v) SETIDE(i) ║ ╚════════════════════════════════════╝ Description: manages the data (attribute and identity) of the current entity. Attributes are floating point numbers. Identity is an integer, often set by last parameter of CREATE(g,i) or SCHED(g,e,i) when the present entity was CREATEd or SCHEDuled. A returns the n-th attribute (floating point number); IDE returns the identity (integer); SETA sets the n-th attribute's value to v; SETIDE sets identity to i. Arguments: n: (integer) attribute index, n = 1,...,max_atr where max_atr is second argument of INIQUE(q,max_atr,s). v: (floating point number) any value. i: (integer) any value. Mandatory predecessors: INIQUE(q,max_atr,s), and one of: NEXTEV(), REMVFC(r), REMVFQ(m,r). Forbidden predecessors: DISPOS(), QUEUE(m,p), SCHED(g,e,i). Recommanded predecessor for A: SETA(n,v), for IDE: one of - SETIDE(i), CREATE(g,i) or SCHED(g,e,i). Errors: if there is no current entity. For A and SETA also if n < 1 or n > max_atr. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 0,2,0 ║INIQUE(0,2,0);║ call INIQUE(0,2,0)║INIQUE(0,2,0);║ ║CREATE 0,0 ║CREATE(0,0); ║ call CREATE(0,0) ║CREATE(0,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e = NEXTEV; ║ ║SETA 2,7 ║SETA(2,7); ║ call SETA(2,7) ║SETA(2,7); ║ ║SETIDE 99 ║SETIDE(99); ║ call SETIDE(99) ║SETIDE(99); ║ ║print A(1),_ ║printf( ║ write (*,*) ║writeln( ║ ║A(2),IDE ║"%f, %f %d\n",║+A(1),A(2),IDE() ║A(1),' ', ║ ║ ║A(1),A(2), ║ ║A(2),' ',IDE);║ ║ ║IDE()); ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A single entity is CREATEed and made current by NEXTEV. 1st attribute is not initialized, 2nd one is initialized to 7 and the identity to 99. Then all of them are printed out. SSS Reference Page 8 ╔══════════════════════════════════════╗ ║ AIC(r,n), IDIC(r), NEIC(r), TIC(r) ║ ╚══════════════════════════════════════╝ Description: returns data about the r-th entity in calendar (Attributes are like the latest current ones just prior SCHEDuling the entity.) - AIC returns the n-th attribute (as a floating point number); IDIC returns the identity code (last argument in CREATE or SCHED, an integer); NEIC returns the next event code (1 for CREATE, 2nd argument in SCHED, an integer); TIC returns the simulated time of the next event (first argument in CREATE/SCHED + simulated time when CREATE/SCHED was called, a floating point number). Arguments: r (integer) is the rank of entity in calendar, r = 1,...,NC(), where NC() is the number of entities in the calendar. n (integer) is the attribute index, n = 1,...,max_atr, where max_atr is second argument of INIQUE(q,max_atr,s). Mandatory predecessors: INIQUE(q,max_atr,s) and either CREATE(g,i) or SCHED(g,e,i). Recommended predecessor for AIC: SETA(n,v) Errors: if r < 1 or r > NC() or when calendar is empty or is not yet created. For AIC also when n < 1 or n > max_atr Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 0,2,0 ║INIQUE(0,2,0);║ call INIQUE(0,2,0)║INIQUE(0,2,0);║ ║CREATE 0,0 ║CREATE(0,0); ║ call CREATE(0,0) ║CREATE(0,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e = NEXTEV; ║ ║SETA 2,7 ║SETA(2,7); ║ call SETA(2,7) ║SETA(2,7); ║ ║SCHED 9,2,0 ║SCHED(9,2,0); ║ call SCHED(9,2,0) ║SCHED(9,2,0); ║ ║print _ ║printf( ║ write (*,*) ║writeln( ║ ║AIC(1,2) _ ║"%f %f %d %d",║+AIC(1,2),TIC(1), ║AIC(1,2), ║ ║TIC(1) _ ║AIC(1,2), ║+NEIC(1),IDIC(1) ║TIC(1),NEIC(1)║ ║NEIC(1) ║TIC(1),NEIC(1)║ ║,IDIC(1)); ║ ║IDIC(1) ║,IDIC(1)); ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A single entity is CREATEed and made current by NEXTEV. 1st attribute is not initialized, 2nd one is initialized to 7. After initialization the entity is SCHEDuled, thus put to the calendar. Since this is the only entity its rank in the calendar is 1. The data of the entity are printed out from the calendar. SSS Reference Page 9 ╔════════════════════════════════════╗ ║ AIQ(m,r,n), IDIQ(m,r), PRIQ(m,r) ║ ╚════════════════════════════════════╝ Description: returns data about the r-th entity in queue m. Attributes and id are like the latest current ones just prior placing the entity to the queue - AIQ returns the n-th attribute (as a floating point number); IDIQ returns the identity code (as an integer); PRIQ returns the priority (second argument in QUEUE which placed this entity to queue, a floating point number) Arguments: m (integer) is the queue index, m = 1,...,max_que, where max_que is the first argument in INIQUE(max_que,max_atr,s). r (integer) is the rank of entity in calendar, r = 1,...,NQ(m), where NQ(m) is the number of entities in queue m. n (integer0 is the attribute index, n = 1,...,max_atr, where max_atr is second argument of INIQUE(max_que,max_atr,s). Mandatory predecessors: INIQUE(max_que,max_atr,s) and QUEUE(m,p). Recommended predecessor: for AIQ: SETA(n,v) Errors: if m < 1 or m > max_que or r > NQ(m). For AIQ also if n < 1 or n > max_atr. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 3,2,0 ║INIQUE(3,2,0);║ call INIQUE(3,2,0)║INIQUE(3,2,0);║ ║CREATE 0,0 ║CREATE(0,0); ║ call CREATE(0,0) ║CREATE(0,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e = NEXTEV; ║ ║SETA 2,7 ║SETA(2,7); ║ call SETA(2,7) ║SETA(2,7); ║ ║QUEUE 3,0 ║QUEUE(3,0); ║ call QUEUE(3,0) ║QUEUE(3,0); ║ ║print _ ║printf("%f\n",║ write (*,*) ║writeln( ║ ║AIQ(3,1,2) ║AIQ(3,1,2)); ║+AIQ(3,1,2) ║AIQ(3,1,2)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A single entity is CREATEed and made current by NEXTEV. 1st attribute is not initialized, 2nd one is initialized to 7. After initialization the entity is placed to queue #3. Since this is the only entity its rank in the queue is 1. The value of the attribute # 2 is printed out from the queue. SSS Reference Page 10 ╔═══════════╗ ║ BE(W,U) ║ ╚═══════════╝ Description: returns a continuous random beta variate (as a floating point number) whose mean is W/(U + W) Arguments: W (positive floating point number) is a shape parameter. U (positive floating point number) is a shape parameter. Errors: when U or W are not positive. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║BE(2,1) ║BE(2,1)); ║+BE(2,1) ║BE(2,1); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A random variate from BE(2,1) distribution is printed out. The probability density function of BE(2,1) is f(x) = 2x (0 < x < 1). ╔══════════════════╗ ║ BI(N,P), NP(M) ║ ╚══════════════════╝ Description: returns a discrete random variate (as integer) according to the distribution law - BI binomial, number of successful trials out of N NP Poisson, binomial with many trials when probability of success in each trial is small. Arguments: N (positive integer) is the number of trials. P (a positive floating point number less than 1) is the probability of success in one trial. M (positive floating point number) is the mean number of successes. Errors: when N or P or M are not positive or P > 1. ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║BI(4,.2) ║BI(4,.2)); ║+BI(4,.2) ║BI(4,.2); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A random variate from BI(4,.2) distribution is printed out. This is the number of successes in 4 trials when the probability of success for each trial is 1/5. SSS Reference Page 11 ╔══════════════════════╗ ║ CD(X,V,N), DP(V,N) ║ ╚══════════════════════╝ Description: Returns a continuous/discrete random variate according to user defined distribution - CD for continuous case; DP for discrete case. Arguments: X (floating point array) is the ordinates. V (floating point array) is the cumulative probabilities. N (integer) is the number of elements in X and V. Notes on the arguments: The elements of X and V must constitute increasing sequences. The probability that a continuous random variable is X[i] or less is V[i], i=1,...,N (for FORTRAN & Pascal or i=0,...N-1 for BASIC & C). The probability that a discrete random variable is i-1 (for FORTRAN & Pascal or i for BASIC & C) or less is V[i]. Note on starting index: it is the index of array natural to the language: 0 for BASIC and C, 1 for FORTRAN and Pascal. Note on BASIC: for each array we pass TWO integers, the first must be varptr(<array's first element>) while the second is varseg(<array's first element>). Take care to add # to X and V, the compiler cannot correct it as in other cases! Note on Pascal: the array's type is user_arr. This type is already defined in the Pascal unit or SSSP2.H. Examples: ╔════════════════╦══════════════╦════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠════════════════╬══════════════╬════════════════╬══════════════╣ ║ ║ ║ real*8 x(3) ║ ║ ║x#(0)=0:p#(0)=0 ║double x[3], ║ real*8 p(3) ║var ║ ║x#(1)=3:p#(1)=.3║p[3]; ║ x(1)=0 ║x,p: user_arr;║ ║x#(2)=4:p#(2)=1 ║x[0]=0;p[0]=0;║ x(2)=3 ║x[1]=0;p[1]=0;║ ║ix=varptr(x#(0))║x[1]=3; ║ x(3)=4 ║x[2]=3; ║ ║ip=varptr(p#(0))║p[1]=.3; ║ p(1)=0 ║p[2]=.3; ║ ║sx=varseg(x#(0))║x[2]=4;p[2]=1;║ p(2)=.3 ║x[3]=4;p[3]=1;║ ║sp=varseg(p#(0))║printf("%f ", ║ p(3)=1 ║writeln( ║ ║print CD(ix,_ ║CD(x,p,3)); ║ write(*,*) ║CD(x,p,3), ║ ║sx,ip,sp,3), ║printf("%f\n",║+CD(x,p,3), ║DP(p,3)); ║ ║DP(ip,sp,3) ║DP(p,3)); ║+DP(p,3) ║ ║ ╚════════════════╩══════════════╩════════════════╩══════════════╝ Explanation: A continuous distribution is defined for which the probability of 2 or less is 0.2, the probability of 3.5 or less is 0.65, etc. A pseudo random variate is generated and printed out for this distribution. DP reflects a distribution function for which the probability for 1 is .3 and for 2 is .7. SSS Reference Page 12 ╔══════════════════════════════════════════════════════════╗ ║ CLEARQ(m), QAVG(m), QMAX(m), QMIN(m), QNUM(m), QSTD(m) ║ ╚══════════════════════════════════════════════════════════╝ Description: managing statistical information about size of queue m. Routines starting with Q return time persistent statistics (as floating point numbers) since the start of simulation or latest CLEARQ, whatever is later - CLEARQ clears statistic of a queue or of all queues; QAVG returns time average; QMAX returns maximum queue size; QMIN returns minimum queue size; QNUM returns length of period for which statistic is accumulated; QSTD returns standard deviation of queue size. Argument: (integer) is the queue index, m = 1,...,max_que, where max_que is the first argument in INIQUE(max_que,b,s). Only for CLEARQ m=0 is allowed, calling CLEARQ(0) clears the statistics of all the queues while if m = 1,...,max_que it clears statistics of queue m only. Mandatory predecessor: INIQUE(max_que,b,s) except for CLERQ(0). Recommanded predecessors: INIQUE(max_que,b,s), QUEUE(m,p) and REMVFQ(m,r) Errors: if m < 1 or m > max_que, except for CLEARQ(0). Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 3,0,0 ║INIQUE(3,0,0);║ call INIQUE(3,0,0)║INIQUE(3,0,0);║ ║CREATE 0,0 ║CREATE(0,0); ║ call CREATE(0,0) ║CREATE(0,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e = NEXTEV; ║ ║QUEUE 3,0 ║QUEUE(3,0); ║ call QUEUE(3,0) ║QUEUE(3,0); ║ ║SETT(3) ║SETT(3); ║ call SETT(3) ║SETT(3); ║ ║REMVFQ(3,1) ║REMVFQ(3,1); ║ call REMVFQ(3,1) ║REMVFQ(3,1); ║ ║print _ ║printf("%f\n",║ write (*,*) ║writeln( ║ ║QAVG(3) ║QAVG(3)); ║+QAVG(3) ║QAVG(3)); ║ ║CLAERQ(3) ║CLEARQ(3); ║ CLEARQ(3) ║CLEARQ(3); ║ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║QAVG(3) ║QAVG(3)); ║+QAVG(3) ║QAVG(3)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A single entity is CREATEed and made current by NEXTEV. An entity is placed on QUEUE #3, the simulated time is increased to 3 (from initial 0 when the QUEUEing took place) and removed from QUEUE 3. The average queue size is printed out before and after CLEARing the Queue statistics of that queue. SSS Reference Page 13 ╔═════════════════════════╗ ║ CLEARS(j), TALLY(j,v) ║ ╚═════════════════════════╝ Description: managing statistics j - CLEARS clears statistics of a variable or of all the variables; TALLY collects observations (for a stochastic process it has to be called after each change of the variable). Arguments: j (integer) the variable's index, j = 1,...,max_sta (integer) where max_sta is the third argument in INIQUE(q,b,max_sta). Only for CLEARS j=0 is allowed, calling CLEARS(0) clears the all the statistics managed by the user, while if j = 1,...,max_sta it clears statistics of variable j only. v (floating point number) is a new observation of the variable. Mandatory predecessors: INIQUE(q,b,max_sta) and INISTA(j,h,k,l,w) Errors: if j < 1 or j > max_sta except for CLEARS(0). Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║x$="1st ║ ║ ║ ║ ║INIQUE 0,0,1 ║INIQUE(0,0,1);║ call INIQUE(0,0,1)║INIQUE(0,0,1);║ ║INISTA(1,_ ║INISTA(1, ║ call INISTA(1, ║INISTA(1, ║ ║sadd(x$),0,_ ║"1st",0, ║+'1st ║'1st',0, ║ ║0,0,0) ║0,0,0) ║+0,0,0,0) ║0,0,0) ║ ║TALLY(1,4) ║TALLY(1,4); ║ call TALLY(1,4) ║TALLY(1,4); ║ ║print _ ║printf("%f\n",║ write (*,*) ║writeln( ║ ║SAVG(1) ║SAVG(1)); ║+SAVG(1) ║SAVG(1)); ║ ║CLAERS(1) ║CLEARS(1); ║ CLEARS(1) ║CLEARS(1); ║ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║SAVG(1) ║SAVG(1)); ║+SAVG(1) ║SAVG(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One statistic collection is initialized by INIQUE and INISTA (see there particulars). One sample of one observation is recorded. The average is printed out before and after clearing the statistic. SSS Reference Page 14 ╔═══════════════╗ ║ CREATE(g,i) ║ ╚═══════════════╝ Description: Creates a new entity by placing it to the calendar with event code 1. Arguments: g (non-negative floating point number) is the simulated time duration between creation and entity's arrival. i (integer) is the identity code of that created entity. Remarks: A new entity can be entered to the system only by CREATE(g,i) and actually arrive only after NEXTEV() is called. Then the entity becomes current. CREATE(g,i) does not affect the current entity (if exists) in any way. (Current entity can be placed to the calendar by SCHED(g,e,i).) CREATE(g,i) takes care to "refill" the calendar with new entities as opposed to NEXTEV() which "depletes" it. It is essential to call it at least once before the event loop, otherwise NEXTEV() finds an empty calendar and no simulation takes place. Mandatory predecessor: INIQUE(q,b,s). Errors: calendar is not yet created. Note: if g is found negative, it is corrected to 0 automatically. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 0,2,0 ║INIQUE(0,2,0);║ call INIQUE(0,2,0)║INIQUE(0,2,0);║ ║CREATE 0,0 ║CREATE(0,0); ║ call CREATE(0,0) ║CREATE(0,0); ║ ║print IDIC(1)║printf("%f\n",║ write (*,*) ║writeln( ║ ║ ║IDIC(1)); ║+IDIC(1) ║IDIC(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A single entity is CREATEed and its identity is printed out. SSS Reference Page 15 ╔════════════╗ ║ DISPOS() ║ ╚════════════╝ Description: disposes a current entity. Remarks: DISPOS() is called when an entity leaves the system. If there is no current entity, DISPOS has no effect. After DISPOS is called there is no current entity. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║INIQUE 0,0,1 ║INIQUE(0,0,1);║ call INIQUE(0,0,1)║INIQUE(0,0,1);║ ║CREATE 2,0 ║CREATE(2,0); ║ call CREATE(2,0) ║CREATE(2,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║DISPOS ║DISPOS(); ║ call DISPOS ║DISPOS; ║ ║DISPOS ║DISPOS(); ║ call DISPOS ║DISPOS; ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One entity is created which arrives at simulated time 2, and is immediately disposed. The second calling of DISPOS does not cause an error, but does nothing either. ╔════════════════════════════════════╗ ║ ER(M,K), EX(M), GA(M,K) WE(M,U) ║ ╚════════════════════════════════════╝ Description: returns a continuous random variate (as a floating point number) according to distribution law - ER Erlang [with mean K*M] EX exponential GA gamma [with mean K*M] WE Weibull [X to power of U is exponential with mean M] Arguments: U (positive floating point number) is a shape parameter. M (positive floating point number) is the exponential mean K for ER (positive integer): is number of stages for GA (positive floating point number): is generalized number of stages. Errors: when U or K or M are not positive. ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║WE(1,2) ║WE(1,2)); ║+WE(1,2) ║WE(1,2); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A random variate from WE(1,2) distribution is printed out. The probability density function of WE(1,2) is f(x) = 2x * exp( - x*x). SSS Reference Page 16 ╔═════════════════╗ ║ INIQUE(q,b,s) ║ ╚═════════════════╝ Description: initiates the calendar, q queues, b attributes and s statistics. All the parameters are integers. Remark: Except for the random generators or T(), SETT(g), all the routines need INIQUE(q,b,s), so be sure to include it at the setup stage of simulation. Warnings: if q or b or s are higher than preset limits. Forbidden predecessor: INIQUE(q,b,s). Errors: if any of the parameters are negative or called more than once. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║INIQUE 3,2,1 ║INIQUE(3,2,1);║ call INIQUE(3,2,1)║INIQUE(3,2,1);║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: maximum 3 queues, 2 attribute and one variable's statistics collection by TALLY(j,v) are possible. ╔══════════════════════╗ ║ INISTA(j,h,k,l,f,w) ║ ╚══════════════════════╝ Description: initialization of statistics collecting and standard report (by calling SUMRY(u)) for a variable. Arguments: j (integer) the variable's index, j = 1,...,max_sta (integer) where max_sta is the third argument in INIQUE(q,b,max_sta). h (str20, e.i. a string with 20 charcters maximum) is used as a headline in SUMRY when printing out results. See notes further. k (integer) is 1 for a stochastic process, 0 for an ordinary variable. l (integer) is number of cells in the observations' histogram printed in SUMRY(u). l=0 if no histogram is required. f (floating point number) is the lower bound of the first cell in the histogram. w (floating point number) is the width of a cell in the histogram. SSS Reference Page 17 Remarks: a stochastic process is a random variable which changes at some points of time and we are interested in its time average rather than its simple average. An example is inventory: if first three days we have 5 units, and the fourth day only 3 then the time average is (5*3 + 3*1)/4 = 4.5 and while the simple average is (5 + 3)/2 = 4. Thus, set third parameter (k) to 1 to get 4.5, while if k is 0, the result is 4. Independent of the value of l, no histogram is produced for a stochastic process. If no histogram is generated (either because k=1 or l=0), f and w can have any value. Note for BASIC: the second argument (headline) in BASIC should be sadd(x$) where x$ is a string defined prior to calling INISTA with 20 characters. If the length of headline is shorter, pad it with spaces. Note for FORTRAN: place the second argument (headline) as a string constant with 20 characters. If the length of headline is shorter, pad it with spaces. Mandatory predecessor: INIQUE(q,b,max_sta). Forbidden predecessor for INISTA(j,...): INISTA(j,...) with the same j. Errors: if j < 1 or j > max_sta or calling INISTA twice with first argument equal. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║x$="1st ║ ║ ║ ║ ║INIQUE 0,0,1 ║INIQUE(0,0,1);║ call INIQUE(0,0,1)║INIQUE(0,0,1);║ ║INISTA(1,_ ║INISTA(1, ║ call INISTA(1, ║INISTA(1, ║ ║sadd(x$),0,_ ║"1st",0, ║+'1st ║'1st',0, ║ ║0,0,0) ║0,0,0) ║+0,0,0,0) ║0,0,0) ║ ║TALLY(1,4) ║TALLY(1,4); ║ call TALLY(1,4) ║TALLY(1,4); ║ ║print _ ║printf("%f\n",║ write (*,*) ║writeln( ║ ║SAVG(1) ║SAVG(1)); ║+SAVG(1) ║SAVG(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One statistic collection is initialized by INIQUE and INISTA (see there particulars). One sample of one observation is recorded. The average is printed out. SSS Reference Page 18 ╔═══════════════╗ ║ NC(), NQ(m) ║ ╚═══════════════╝ Description: returns number of entities (as integer) in - NC(): the calendar NQ(m): queue number m. Argument in NQ: m (integer) is the index of queue, m = 1,...max_que, where max_que is first argument in INIQUE(max_que,b,s). Mandatory predecessor: INIQUE(max_que,b,s). Error: for NC if calendar is not yet initialized by INIQUE(), for NQ if m < 1 or m > max_que. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║CREATE 2,0 ║CREATE(2,0); ║ call CREATE(2,0) ║CREATE(2,0); ║ ║print NC ║printf("%d\n",║ write(*,*) NC() ║writeln(NC); ║ ║ ║NC()); ║ ║ ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║QUEUE(1,0) ║QUEUE(1,0.0); ║ call QUEUE(1,0) ║QUEUE(1,0); ║ ║print NQ(1) ║printf("%d\n",║ write(*,*) NQ(1) ║writeln( ║ ║ ║NQ(1)); ║ ║NQ(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One entity is created (=placed on calendar) and number of entities in the calendar is printed out. Then the same entity is made current by NEXTEV, placed on queue #1 and the number of entities in that queue is printed out. SSS Reference Page 19 ╔════════════════════╗ ║ NCEN(), NEXTEV() ║ ╚════════════════════╝ Description: NCEN() returns 0 or 1 depending whether there is no current entity (=0) or there is one (=1). There cannot be more than one current entity. There must be a current entity before calling one of: A, IDE, QUEUE, SCHED, SETA, SETIDE. There must not be a current entity before calling one of: NEXTEV, REMVFC, REMVFQ. NEXTEV() removes the first entity from the calendar, makes it current, moves forward the simulated time if the event time of this entity is later and returns the event code of this entity as a non-negative integer. Remarks: NEXTEV() is the chief driver of the simulation. It is at the top of the event loop. Mandatory predecessors for NEXTEV(): one of INIQUE(q,b,s), SCHED(g,e,i), QUEUE(m,p). Forbidden predecessors for NEXTEV(): NEXTEV(), REMVFC(r), REMVFQ(m,r). Recommended predecessor for NEXTEV(): CREATE(g,i). Errors for NEXTEV(): if the calendar has not been initiated by INIQUE or there is a current entity. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 0,0,1 ║INIQUE(0,0,1);║ call INIQUE(0,0,1)║INIQUE(0,0,1);║ ║print NCEN ║printf("%d\n",║ write(*,*)NCEN() ║writeln(NCEN);║ ║ ║NCEN()); ║ ║ ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: The calendar is empty after initialized by INIQUE, therefore e is 0. Also NCEN returns 0 as there is no current entity. SSS Reference Page 20 ╔═══════════════════════╗ ║ QDC(m), SETQDC(m,d) ║ ╚═══════════════════════╝ Description: the discipline of queue number m is - QDC: returned as a character (one of: F, L, B, S) SETQDC: set (to one of FIFO, LIFO, BVF, SVF). Arguments: m (integer) is the index of queue, m = 1,...max_que where max_que is the first argument in INIQUE(max_que,b,s). d (str6, e.i. a string with 6 charcters maximum) is the discipline, one of: FIFO, LIFO, BVF, SVF. If d is any other string (like bvs or KKK), the first character counts. If it is L or B or S, the discipline is treated as LIFO or BVF or SVF respectively. If it is different (like b or K) it is treated as FIFO. Note for BASIC: the second argument of SETQDC (discipline) in BASIC should be sadd(x$) where x$ is a string defined prior to calling SETQDC with 6 characters. If the length of discipline is shorter, pad it with spaces. Note for FORTRAN: place the second argument of SETQDC (discipline) as a string constant with 6 characters. If the length of discipline is shorter, pad it with spaces. Mandatory predecessor: INIQUE(max_que,b,s). Errors: if m < 1 or m > max_que. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║x$="B " ║ ║ ║ ║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║SETQDC(1,_ ║SETQDC(1,"B");║ call SETQDC(1, ║SETQDC(1,'B');║ ║sadd(x$)) ║ ║+'B ') ║ ║ ║print QDC(1) ║printf("%c\n",║ write(*,*) QDC(1) ║writeln( ║ ║ ║QDC(1)); ║ ║QDC(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: The discipline is set to "B", printed out. This discipline is interpreted as Biggest Value First. SSS Reference Page 21 ╔══════════════╗ ║ QUEUE(m,p) ║ ╚══════════════╝ Description: places the current entity in queue number m with priority p. According to queue discipline FIFO/LIFO/SVF/ BVF which has been set most recently by SETQDC. (If none is set the default is FIFO.) After calling QUEUE there is no current entity. Arguments: m (integer) is the index of queue, m = 1,...max_que where max_que is first argument in INIQUE(max_que,b,s). p (floating point number) is the priority. Argument has effect only with disciplines SVF or BVF. The rank of the the entity in the queue is such that in SVF the entity with Smallest Value of p is First and in BVF the entity with Biggest Value of p is First. Mandatory predecessor: INIQUE(max_que,b,s) and one of: NEXTEV(), REMVFC(r), REMVFQ(m,r). Forbidden predecessors: DISPOS(), QUEUE(m,p), SCHED(g,e,i). Errors: if there is no current entity or m < 1 or m > max_que. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║CREATE 2,0 ║CREATE(2,0); ║ call CREATE(2,0) ║CREATE(2,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║QUEUE(1,0) ║QUEUE(1,0.0); ║ call QUEUE(1,0) ║QUEUE(1,0); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One entity is created (=placed on calendar) and is made current by NEXTEV. The current entity is placed on queue #1. SSS Reference Page 22 ╔══════════════════════════════════════════════╗ ║ RA(), RL(M,S), RN(M,S), TR(I,B,C), UN(I,C) ║ ╚══════════════════════════════════════════════╝ Description: returns a continuous random variate (as a floating point number) according to distribution law - RA uniform between 0 and 1 RL log-normal, so that after taking natural logarithm, the resulting distribution is normal with mean M, standard deviation S (S > 0) RN normal with mean M, standard deviation S (S > 0) TR triangular between I and C with mode B UN uniform between I and C. Arguments are all floating point numbers. Errors: when C < B or B < I. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║RN(2,1) ║RN(2,1)); ║+RN(2,1) ║RN(2,1); ║ ║print _ ║printf("%f\n",║ write(*,*) ║writeln( ║ ║TR(0,3,4) ║TR(0,3,4)); ║+TR(0,3,4) ║TR0,3,4)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: A random normal variate is printed from a distribution with mean 2 and standard deviation 1. Then a random variate from TR(0,3,4) is printed out. SSS Reference Page 23 ╔══════════════════════════╗ ║ REMVFC(r), REMVFQ(m,r) ║ ╚══════════════════════════╝ Description: making an entity (which has had rank r) current by removing it from - REMVFC: calendar; REMVFQ: queue number m. Arguments: r (integer) is the rank of entity - for REMVFC: in calendar, r = 1,...,NC(), where NC() is number of entities in calendar; for REMVFQ: in queue m, r = 1,...,NQ(m), where NQ(m) is the number of entities in queue m. m (integer) is the index of queue, m = 1,...max_que, where max_que is first argument in INIQUE(max_que,b,s). Mandatory predecessors: INIQUE(q,b,s), for REMVFC also one of: CREATE(g,i), SCHED(g,e,i), for REMVFQ also QUEUE(m,p). Forbidden predecessor: NEXTEV(), REMVFC(r), REMVFQ(m,r). Errors: if prior to call there is a current entity or calendar is not initiated by INIQUE(max_que,b,s) or if m > max_queue or (for REMVFQ) r > NQ(m) or (for REMVFC) r > NC(). Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║CREATE 0,1 ║CREATE(0,1); ║ call CREATE(0,1) ║CREATE(0,1); ║ ║CREATE 2,2 ║CREATE(2,2); ║ call CREATE(2,2) ║CREATE(2,2); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║QUEUE 1,0 ║QUEUE(1,0.0); ║ call QUEUE(1,0) ║QUEUE(1,0); ║ ║REMVFQ 1,1 ║REMVFQ(1,1); ║ call REMVFQ(1,1) ║REMVFQ(1,1); ║ ║DISPOS ║DISPOS(); ║ call DISPOS ║DISPOS; ║ ║REMVFC 1,1 ║REMVFC(1,1); ║ call REMVFC(1,1) ║REMVFC(1,1); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Two entities are created (=placed on calendar). The first is made current and placed to queue #1. Then the remaining one is removed from the calendar, disposed and the one in the queue is removed next. Note that without intermingled DISPOS this could cause an error. SSS Reference Page 24 ╔═══════════════════════════════════════════════╗ ║ SAVG(j), SMAX(j), SMIN(j), SNUM(j), SSTD(j) ║ ╚═══════════════════════════════════════════════╝ Description: returning statistics about about variable j as floating point numbers since the start of simulation or latest CLEARS, whatever is later - SAVG average (or time average for a stochastic process); SMAX maximum observed value; SMIN minimum observed value; SNUM sample size (for a stochastic process the length of period is returned for which statistics are accumulated); SSTD standard deviation of observed values calculated as the square root of the sum of deviations from SAVG devided by SNUM. Note that the demoninator is the sample size rather than the degrees of freedom! Argument: j (integer) the variable's index, j = 1,...,max_sta (integer) where max_sta is the third argument in INIQUE(q,b,max_sta). Mandatory predecessors: INIQUE(q,b,max_sta) and INISTA(j,h,k,l,w) Recommended predecessor: TALLY(j,v). Errors: if j < 1 or j > max_sta. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║x$="1st ║ ║ ║ ║ ║INIQUE 0,0,1 ║INIQUE(0,0,1);║ call INIQUE(0,0,1)║INIQUE(0,0,1);║ ║INISTA(1,_ ║INISTA(1, ║ call INISTA(1, ║INISTA(1, ║ ║sadd(x$),0,_ ║"1st",0, ║+'1st ║'1st',0, ║ ║0,0,0) ║0,0,0) ║+0,0,0,0) ║0,0,0) ║ ║TALLY(1,4) ║TALLY(1,4); ║ call TALLY(1,4) ║TALLY(1,4); ║ ║print _ ║printf("%f\n",║ write (*,*) ║writeln( ║ ║SAVG(1) ║SAVG(1)); ║+SAVG(1) ║SAVG(1)); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: One statistic collection is initialized by INIQUE and INISTA (see there particulars). One sample of one observation is recorded. The average is printed out. SSS Reference Page 25 ╔════════════════╗ ║ SCHED(g,e,i) ║ ╚════════════════╝ Description: the current entity is placed on the calendar with identity i, event code e to be removed from there after g units of simulated time by NEXTEV. If the identity is to be preserved i = IDE(). Arguments: g (non-negative floating point number) is the simulated time that elapses between present and the time that event e is executed; e (integer bigger than 1) is the event code; i (integer) is the identity. Remark: SCHED(g,e,i) "sends" the current entity to its next event e after a delay of g units time from present simulated time. It acts as a kind of delayed "goto". After calling SCHED(g,e,i) there will be no current entity. Therefore delay calling SCHED(g,e,i) to the latest moment consistent with your program. Mandatory predecessors: NEXTEV(), REMVFC(r), REMVFQ(m,r). Forbidden predecessors: DISPOS(), QUEUE(m,p), SCHED(g,e,i). Errors: if prior to call there is already a current entity or e is 0, 1 or negative. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║CREATE 0,1 ║CREATE(0,1); ║ call CREATE(0,1) ║CREATE(0,1); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║SCHED .5,2, _║SCHED(.5,2, ║ call SCHED(.5,2, ║SCHED(.5,2, ║ ║IDE ║IDE()); ║+IDE()) ║IDE); ║ ║print NEXTEV ║printf("%d\", ║ write(*,*)NEXTEV()║writeln( ║ ║ ║NEXTEV()); ║ ║NEXTEV); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: An entity is created (=placed on calendar), made current, scheduled again for time .5 and its event code is printed out. SSS Reference Page 26 ╔════════════════════════╗ ║ SETANT(y), SETSEE(x) ║ ╚════════════════════════╝ Description: routines managing the random stream - SETANT sets(y=1)/resets(y=0) antithetic stream SETSEE sets the random seed to x Arguments: y is 0 or 1. x (positive odd integer) is the seed. Remarks: For other than the above arguments the routines have no effect. ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║SETSEE 777 ║SETSEE(777); ║ call SETSEE(777) ║SETSEE(777); ║ ║SETANT 0 ║SETANT(0); ║ call SETANT(0) ║SETANT(0); ║ ║print EX(1),_║printf( ║ write(*,*) EX(1), ║writeln( ║ ║EX(1) ║"%f %f ", ║+EX(1) ║EX(1),EX(2)); ║ ║ ║EX(1),EX(1)); ║ ║ ║ ║SETSEE 777 ║SETSEE(777); ║ call SETSEE(777) ║SETSEE(777); ║ ║SETANT 1 ║SETANT(1); ║ call SETANT(1) ║SETANT(1); ║ ║print EX(1),_║printf( ║ write(*,*) EX(1), ║writeln( ║ ║EX(1) ║"%f %f ", ║+EX(1) ║EX(1),EX(2)); ║ ║ ║EX(1),EX(1)); ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Two pairs of antithetic exponential variates are printed. Note that the seed had to be reset to 777. SSS Reference Page 27 ╔═══════════════════════╗ ║ SETDEB(o), SHOWQ(m) ║ ╚═══════════════════════╝ Description: routines for debug - SETDEB sets switches which tell what to do after an error or when to print out calendar and/or queues SHOWQ shows contents of queue m or the calendar (m=0) Arguments: o (integer between 0 and 15) with following significance (3 is the default; stop means immediate stop): ╔══════════════════════════════════════════════════════════════╗ ║o = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15║ ║stop on error? N Y N Y N Y N Y N Y N Y N Y N Y║ ║print error? N N Y Y N N Y Y N N Y Y N N Y Y║ ║print calendar? N N N N Y Y Y Y N N N N Y Y Y Y║ ║print queues? N N N N N N N N Y Y Y Y Y Y Y Y║ ╚══════════════════════════════════════════════════════════════╝ m (integer) is the index of queue, m = 1,...max_que, where max_que is first argument in INIQUE(max_que,b,s) or m=0 for the calendar. Remarks: calendar and queue is printed just before removing an entity from them. Any other value for o does not have any affect. See further discussion on errors under SIMERR(). Note for FORTRAN: If you write to screen before the calendar or queue, include an end of line in your write command, otherwise the calendar's or queues' first line will be on the last written line. Mandatory predecessor for SHOWQ(m): INIQUE(max_que,b,s). Errors for SHOWQ: if m > max_queue or m < 0. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║SETDEB 15 ║SETDEB(15); ║ call SETDEB(15) ║SETDEB(15); ║ ║CREATE 0,1 ║CREATE(0,1); ║ call CREATE(0,1) ║CREATE(0,1); ║ ║CREATE 2,2 ║CREATE(2,2); ║ call CREATE(2,2) ║CREATE(2,2); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║QUEUE 1,0 ║QUEUE(1,0.0); ║ call QUEUE(1,0) ║QUEUE(1,0); ║ ║SHOWQ 1 ║SHOWQ(1); ║ call SHOWQ(1) ║SHOWQ(1); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Two entities are created (=placed on calendar). The first is made current and placed to queue #1. Printout should follow NEXTEV and SHOWQ. SSS Reference Page 28 ╔════════════════╗ ║ SETT(g), T() ║ ╚════════════════╝ Description: managing simulated time - SETT sets simulated time to g, T returns current simulated time (as a floating point number). g (floating point number) new absolute value of simulated time, g should not be less than T() prior to calling SETT. Remarks: At start of simulation simulated time is set to 0. If g is less than T() prior to calling SETT, SETT has no effect. Simulated time is managed in general by NEXTEV when it sets the time to next event's time. Next event's times are the first arguments in CREATE(g,i) or SCHED(g,e,i). Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║SETT 7.4 ║SETT(7.4); ║ call SETT(7.4) ║SETT(7.4); ║ ║print T ║printf("%f\", ║ write(*,*) T() ║writeln(T); ║ ║ ║T()); ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Time is set to 7.4 and printed out. SSS Reference Page 29 ╔═════════════╗ ║ SIMEND(g) ║ ╚═════════════╝ Description: Causes end of simulation at absolute simulated time g or immediately if g < T() prior calling SIMEND, where T() is the current simulated time. Argument: g (floating point number) is the absolute simulated time to finish simulation. Mandatory predecessor: INIQUE(q,b,s). Error: if calendar has been not initiated by INIQUE(q,b,s). Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║integer e ║int e; ║ integer e ║var e:integer;║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║SIMEND 9.5 ║SIMEND(9.5); ║ call SIMEND(9.5) ║SIMEND(9.5); ║ ║CREATE 10,0 ║CREATE(10,0); ║ call CREATE(10,0) ║CREATE(10,0); ║ ║e = NEXTEV ║e = NEXTEV(); ║ e = NEXTEV() ║e := NEXTEV; ║ ║print e ║printf("%d\n",║ write(*,*) e ║writeln(e); ║ ║ ║e); ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Two entities are created (=placed on calendar). The first is made current and placed to queue #1. Printout should follow NEXTEV and SHOWQ. SSS Reference Page 30 ╔════════════╗ ║ SIMERR() ║ ╚════════════╝ Description: Returns latest SSS error code as an integer and clears it (clear means 0). Remarks: SIMERR() is in effect only when o is EVEN in SETDEB(o), as for odd values of o the simulation stops on an error. If an error occurs, o is even and SIMERR() is not called then NEXTEV() returns 0 upon its next call, effectively stopping simulation. However, when SIMERR() is called just before NEXTEV(), SIMERR() clears the error and NEXTEV() will continue if possible. This gives to the experianced programmer more control on errors. Note on QuickBASIC v4.5 and similar integrated environments that exit to DOS upon an SSS error: in the beginning of the program include the line SETDEB(2). The meaning of SSS error codes are: ╔════╦══════════════════════════════════════════════════════════╗ ║Code║ Meaning ║ ╠════╬══════════════════════════════════════════════════════════╣ ║ 1 ║ Attempt to make more than one entity current ║ ║ 2 ║ Lack of space in memory ║ ║ 3 ║ Too many entities ║ ║ 4 ║ Queue index is too big or smaller than 1 ║ ║ 5 ║ No entity exists with specified rank and/or queue number ║ ║ 6 ║ There is no current entity when one is needed ║ ║ 7 ║ INIQUE was not called ║ ║ 8 ║ Statistics index is too big smaller than 1 ║ ║ 9 ║ INISTA is called twice with same first argument ║ ║ 10 ║ Summary file cannot be opened ║ ║ 12 ║ Too large rank for queue or calendar ║ ║ 13 ║ Parameters should be positive ║ ║ 14 ║ In TR the parameters do not obay to min <= mode <= max ║ ║ 15 ║ Attribute number is too big or smaller than 1 ║ ║ 16 ║ Event code should be greater than 1 in SCHED ║ ╚════╩══════════════════════════════════════════════════════════╝ Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║CREATE 10,0 ║CREATE(10,0); ║ call CREATE(10,0) ║CREATE(10,0); ║ ║print SIMERR ║printf("%d\n",║ write(*,*)SIMERR()║writeln( ║ ║ ║SIMERR()); ║ ║ SIMERR); ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: CREATE without prior INIQUE raises error code 7 which is printed. After printing error code is cleared. SSS Reference Page 31 ╔════════════╗ ║ SUMRY(u) ║ ╚════════════╝ Description: To write a standard report to screen (if u is an empty string) or to append to file with name u. The standard report is written for each call of INISTA and for each queue including sample size (duration of recording for time persistent statistics), average, (time average for time persistent statistics), standard deviation, minimum and maximum. If in INISTA(j,h,k,l,f,w) k = 0 and l > 0, a frequency table is also printed. Argument: u (string with an appended space in BASIC & FORTRAN) is either empty or a legitimate file name (path names are OK but not wild cards). Examples for u in FORTRAN: ' ' for screen (SPACE between quotes is mandatory!), 'OUT ' for file OUT (last space is mandatory!). Similar holds for BASIC (but notnecessary in C or Pascal). Note for BASIC: u should be sadd(x$) where x$ is a string defined prior to calling SUMRY(sadd(x$)). Note for FORTRAN: If you write on file u before calling SUMRY(u) place an end of line between, otherwise SUMRY will continue the previous line. Mandatory predecessors: INIQUE(q,b,s), INISTA(j,h,k,l,w,f). Recommended predecessors: QUEUE(m,p), TALLY(j,v). Errors: if no closed file can be found with name u or disk is write protected or diskette door is not closed or not enough disk space space to write to file u. Examples: ╔═════════════╦══════════════╦═══════════════════╦══════════════╗ ║ BASIC ║ C ║ FORTRAN ║ Pascal ║ ╠═════════════╬══════════════╬═══════════════════╬══════════════╣ ║x$="1st ║ ║ ║ ║ ║INIQUE 1,0,1 ║INIQUE(1,0,1);║ call INIQUE(1,0,1)║INIQUE(1,0,1);║ ║INISTA(1,_ ║INISTA(1, ║ call INISTA(1, ║INISTA(1, ║ ║sadd(x$),0,_ ║"1st",0, ║+'1st ║'1st',0, ║ ║0,0,0) ║0,0,0) ║+0,0,0,0) ║0,0,0) ║ ║x$=" " ║SUMRY(""); ║ call SUMRY(' ') ║SUMRY(''); ║ ║SUMRY _ ║ ║ ║ ║ ║sadd(x$) ║ ║ ║ ║ ╚═════════════╩══════════════╩═══════════════════╩══════════════╝ Explanation: Summary report is printed for "1st" variable and the queue.