Page 132 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes Little’s Equation

Using  = c in the definition of the time-averaged statistics, along with Little’s Theorem, we
n
have
n
n c
t
c l  l ( )dt   w  nw
i
n
0
i 1
We can perform similar operations and ultimately have
 n   n   n 
l    w and q    d and x   s 
 c n   c n   c n 

Computational Model

1. The ANSI C program ssq1 implements Algorithm 1.2.1
2. Data is read from the file ssq1.dat consisting of arrival times and service times in the
format

a S
1 1
a S
2 2
. .
. .
. .
a S
n n
Since queue discipline is FIFO, no need for a queue data structure

Example
Running program ssq1 with ssq1.dat

1/r  0.10 and 1/ s  0.14
If you modify program ssq1 to compute l , q, and x
x  0.28

Despite the significant idle time, q is nearly 2.
8.1.2 Two-server Queue Simulation

Two Servers in Series

1. Hypothesis: Nonhomogeneous (t) Poisson arrivals; service at server 1, then by server 2
service for each consumer; service times are RVs with distribution G and G ; no consumers
1 2
after final arrival time T.
2. Instances: Airline checkin, doctor’s office, restaurant.
3. Variables: Time t; counters N , N ; system state SS = (n , n ) = customer #s at server 1,2;
A B 1 2
output (A (i),A (i),D(i)) customer i arrival (for each server) and departure times; event list
1 2
EL = (t , t , t ) next arrival and finishing point times.
A 1 2

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