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APL Simulation of Queuing Systems

IP.com Disclosure Number: IPCOM000087860D
Original Publication Date: 1977-Mar-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 2 page(s) / 48K

Publishing Venue

IBM

Related People

Reisser, M: AUTHOR

Abstract

Many queuing systems of practical interest are related to the recurrence equation L(j+1) = (L(j)-1)/+/ + A(j+1) Where L(j) is the queue length at some suitably chosen epoch j, (a)/+/ = Max {0,a} and A(j) are the number of arrivals between epochs j and j+1. Examples of systems based on equation (1) are . the M/G/1 queue, . a buffer which processes a message at regular intervals called time slots.

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APL Simulation of Queuing Systems

Many queuing systems of practical interest are related to the recurrence equation L(j+1) = (L(j)-1)/+/ + A(j+1) Where L(j) is the queue length at some suitably chosen epoch j, (a)/+/ = Max {0,a} and A(j) are the number of arrivals between epochs j and j+1. Examples of systems based on equation (1) are . the M/G/1 queue, . a buffer which processes a message at regular intervals called time slots.

A more complicated system is portrayed in Fig. 1 with a recursion similar to equation (1). Packets are removed in regular intervals called slots.

As shown, X represents the number of high priority packets at node 1, Y represents the number of low priority packets at node 1, and Z represents the number of low priority packets at node 2. The equations for the system of Fig. 1 are X(j) = (X(j-1)-1)/+/ + A(j)/(X)/ Y(j) = (Y(j-1)-X[X(J-1)=0])/+/ + A(j)/(y)/ (2) Z(j) = (Z(j-1)-X[Y(j-1)=0 vX(j-1) does not equal 0])/+/ + A(j)/(Z)/

Where X(B) = (1 if B="true," 0 otherwise). Equation (1) can be solved analytically. It is a system like the one represented by equations (2) which has to be solved by simulation. Since all these ideas can be explained via equation (1), the ensuing discussion will be restricted to this example.

The problem is an efficient simulation of equation (1) on a system like APL which pays a high performance premium on a parallel execution of array operations and which provides a rich set of array operators. Note that a straightforward simu...