SLAM II

Network Elements

Transactions

• Definition - units of traffic flowing through the system
• Attributes are numerical values carried along with a transaction to specify its characteristics:
• ATRIB(I), 1 < = I < = 100

Activities

• Activities (Branches) represent time delays in transaction movement
• Regular activity has unlimited capacity
• Service activity has finite number of parallel servers; must start on a queue node

Nodes

• Nodes mark the start and finish of each activity
• Used to modify transaction flow and the values of network status variables
• The arrival of a transaction at a node defines the only event type in the underlying discrete-event model

Resources

• Resources are finite-capacity system facilities similar to service activities
• Their use is not tied to the traversal of a single branch in the network
• May be allocated and deallocated in any integer amounts
• May be preempted

Gates

• Gates control transaction flow

Global Network Variables

• TNOW = current reading of clock
• XX(I) = global variable I
• SS(I) = state variable I
• DD(I) = time derivative of SS(I)
• NNACT(I) = # of transactions now in activity with label I
• NNCNT(I) = # of transactions that have finished activity I
• NNQ(I) = # of transactions in file I
• NNRSC(I) = unused capacity of resource I
• NNGAT(I) = status of gate I; O if open, 1 if closed

Random Variate Generators

• DRAND - a random number
• UNFRM (a, b) - uniform distribution on [a, b]
• TRIAG (a, m, b) - triangular distribution with minimum = a, mode = m, and maximum = b
• RNORM (u, o) - normal distribution with mean = u and standard deviation = s
• RLOGN (u, o) - lognormal distribution with mean = u and standard deviation = s
• EXPON (u) - exponential distribution with mean = u
• ERLNG (b, a) - Erlang distribution; the sum over a random sample of size a from EXPON ( b )
• GAMA (b , a) - Gamma distribution with shape parameter = a and scale parameter = b
• BETA (h, f) - Beta distribution on the interval [O, I] with shape parameters h and f
• NPSSN (u) - Poisson distribution with mean = u
• WEIBL (b, a) - Weibull distribution with scale parameter = b and shape parameter = a

Activities

1. Branches starting on a QUEUE node are service activities

   Symbol
   
   
   
   
   ACTIVITY (N)/A,DUR,PROB;
   DUR = activity duration; any network variable or random variate
   PROB = probability that transaction will move along this branch
   N = number of parallel servers
   A = integer label , 1 < = A < = 100
   

   
   	Elevator Example
   
   
   	Column:  1	7
   
   			NETWORK;
   			CREATE, 10, 7;
   			ACTIVITY, 3;
   			QUEUE (1);
   				ACTIVITY (1)/3, 9, 0.75, EXIT;
   				ACTIVITY (1)/3, 8.5, 0.25;
   		EXIT	TERMINATE, 100;
   			ENDNETWORK;
   
   

2. Branches not starting on a QUEUE node are regular activities

   

   Symbol
   
   ACTIVITY (N)/A,DUR,PROB COND;
   PROB COND = Fortran-like logical condition involving network variables;
   transaction will move along this branch if condition is true
   

Basic nodes for traffic generation and control

1. Create node - creates entities and routes them into the system over activities that emanate from the CREATE node

   

   CREATE, TBC, TF, MA, MC, M;
   
   mnemonic    definition/comments      default
   
   TF          time of first creation     0.0
   TBC         time between creations   infinity
               can be any network variable
   MA          mark attribute             None
   MC          maximum number of        infinity
               transactions created
   M           M-number
   

   The M-number on the output side of a non-queue node specifies the maximum number of emanating activities which are taken
   1. If there are any probabilistic branches, draw a random number to select a single probabilistic branch
   2. Test conditional branches in the order that they occur and select additional activities to start until the M-number is exhausted
2. Terminate node - terminates (destroys) entities (reclaims disk space used to store information about the entity terminated). The TERMINATE node is used to destry or delte entities from the network.

   

   TERMINATE, TC;
   
   mnemonic    definition/comments                  default
   
   TC    termination counter for this exit point    infinity
   
   

3. Queue node - queue in which entities wait (are queued) A QUEUE is a location in the network where entities wait for service. When an entity arrives at a QUEUE node, its disposition depends on the status of the server that follows the QUEUE node. If the server is idle, the entity passes through the QUEUE node and goes immediately into the service activity. If no server is available, the entity waits in the QUEUE node until a server can process it. When a server becomes available, the entity will automatically be taken out of the queue and service will be initiated.

   When an entity arrives at a QUEUE node which is at its capacity, its disposition must be determined. This decision is based on a specification at the QUEUE node as to whether the entity should balk or be blocked. In the case of balking, the entity can be routed to another node of the network. When an entity is blocked by a QUEUE node, it waits until a free space is available in the queue. The activity which just served the entity that is blocked is also considered as blocked. A blocked entity will join the queue when a space is available.

   

   QUEUE(IFL), IQ, QC;
   
   mnemonic    definition/comments                  default
   
   IQ          initial # in queue                      0
   QC          queue capacity                       infinity
   IFL         file #, 1 < = IFL < = 100
   

4. Accumulate node - entities accumulate at this node; once the specified number have accumulated, an entity is released that represents the group of entities that "accumulated"

   

   ACCUMULATE, FR, SR, SAVE, M;
   
   mnemonic    definition/comments                  default
   
   FR          number of accumulated                   1
               transactions for first release of node
   SR          transaction count required on           1
               subsequent releases
   SAVE        save criterion : FIRST                 LAST
               LAST, HIGH(I), LOW(I),
               SUM, MULT
   

5. Goon node - node used to connect activity branches; provides linkage for activities in series. The GOON node is used in the modeling of sequential activities since 2 consecutive activity statements are used to model parallel activities. Also probabilities and/or deterministic branching can occur following GOON nodes.

   

   GOON, M;
   
   

Operations on network variables

1. Assign node - assigns values to entity or network variables. The ASSIGN node is used to prescribe values to the attributes of an entity passing through the ASSIGN node or to the prescribed values to the system variables that pertain to the network in general.

   

   ASSIGN, VARI = EXP1, VAR2 = EXP2, ..., M;
   
   mnemonic               definition/comments 
   
   VAR1, VAR2, ...    One of the SLAM network variables:
                      ATRIB(I), XX(I), SS(I), DD(I), II
   EXP1, EXP2, ...    Arithmetic expression involving at most 10 of
                      the following:  Network variables, random variables,
                      constants; No parentheses
   

2. COLCT node - tabulate statistics on observations taken during the simulation. The COLCT (collect) node is used to collect statistics on five types of variables: 1) time of all arrivals, 2) time of first arrival, 3) time between arrivals, 4) interval statistics, and 5) a SLAM II variable. For each of the above 5 types of variables, estimates for the mean and standard deviation of the variable are obtained. In addition, a histogram of the values collected at a COLCT node can be obtained.

   

   COLCT, TYPE, ID, NCEL/HLOW/HWID, M;
   
   mnemonic            definition/comments     default
   
   TYPE       observation to be recorded:
              FIRST
              LAST      node arrival times
              BETWEEN
              INTERVAL - time in system
              SLAM network variable
   ID         16 character output label         BLANK
   NCEL       number of interior cells in         0
              histogram to be printed
   HLOW       upper limit of unbounded           0.0
              cell on the left
   HWID       width of interior cells; class     1.0
              interval for empirical frequency
              distribution
   

3. Select node - used to provide branching into a set of queues; determines which queue an entity will enter based on the queue selection rule being used

   

   SLBL	SELECT, QSR,, BALK(NLBL), QLB1, ... ;
   
   mnemonic            definition/comments          default
   
   QSR        Queue selection rule looking forward    POR
              to destination-queues
   BLOCK      Block the service activity ending at  no blocking;
              node SLBL if all destination queues   transaction destroyed
              are full
   BALK(NLBL) Balk to node NLBL if all destination  no balking;
              queues are full	                 transaction destroyed
   QLB1,
   QLB2, ...  Labels of queue nodes to which          ERROR
              transactions are to be routed
   QSR options
     POR      Priority given in preferred order
     CYC      Cyclic priority
     RAN      Random priority
     LAV      priority given to Queue which has had the
              largest average number of entities in it to date
     SAV      priority given to queue which has had the
              smallest average number of entities to date
     LNQ      priority to queue with largest number of entities in queue
     SNQ      priority given to queue with smallest number
              of entities in queue
   

Simulation control statements

1. GEN statement -

   GEN, NAME, PROJECT, MO/DA/YE, NNRNS, ILIST, IECHO
         IXQT, IPIRH, ISMRY, IPR;
   
   mnemonic    definition       options                  default
   
   NAME      Analyst's name  20 alphanumeric characters   Blanks
   PROJECT   Project name    20 characters                Blanks
   MONTH     Month number                                   1
   DAY       Day number                                     1
   YEAR      Year number                                   2001
   NNRNS     Number of runs                                 1
   ILIST     Request for       Y or N                       Y
             input listing
   IECHO     Request for echo  Y or N                       Y
             summary report
   IXQT      Request for       Y or N                       Y
             execution
   IPIRH     Request for       Y or N                       Y
             intermediate results heading
   ISMRY     Request for       Y or N                       Y
             summary reports
   IPR       Print option      72, 130                     130
   

2. LIMITS statement - defines the maximum number of entities and entity attributes (used to assign memory required)

   LIM, MFIL, MATR, MNTRY
   
   mnemonic   definition                        default
   
   MFIL       largest file #                       1
   MATR       maximum # of attributes per entity   0
   MNTRY      maximum # of entries in all files    0
   

3. PRIORITY statement - defines the queue priority rule to be used

   PRIORITY/IFL, RNK/;
   
   mnemonic   definition                        default
   
   IFL        file number                        None
   RNK        file ranking: LVF(I);              FIFO
              HVF(I); FIFO; LIFO
   

4. Seeds statement - assigns a starting seed for a random number stream

   SEEDS, ISEED(ISTRM)/R;
   
   mnemonic   definition                             default
   
   ISEED      integer seed; negative seed yields 
              complimentary sequence of random numbers
   ISTRM      Stream number
   R          reinitialization option (Y or N)          N
   

5. Initialize statement - defines when the simulation begins and stops

   INITIALIZE, TTBEG, TTFIN;
   
   mnemonic   definition                    default
   
   TTBEG      beginning time of run           0.0
   TTFIN      finishing time of run         10 sup 20
   

6. Monitor statement - defines when "monitoring" information is collected; useful for debugging and better understanding a simulation

   MONTR, OPT, TFRST, TBTWN;
   
   mnemonic   definition         options                      default
   
   OPT        monitor option     SUMRY - print summary report  None
                                 FILES - list contents of files
                                 STATES - list SS(.), DD(.) vars
                                 CLEAR - clear statistical arrays
                                 TRACE - trace transaction flow
   TFRST      time of 1st report                                0.0
   TBTWN      time between reports                            10 sup 20
   

7. Simulate statement - indicates that network simulation statements follow

   SIMULATE;
   

8. FIN - signals end of SLAM statements

   FIN;