In this simple queuing model, we use LINGO’s runtime prompt feature to prompt the user for the arrival rate of service customers, the time required by a typical service call and the number of available servers. Once you enter these values, LINGO computes various statistics about the system including using the Erlang busy function (@PEB) to compute the probability a customer must wait for service

MODEL:

! Compute statistics for a multi-server system with

  Poisson arrivals, exponential service time

  distribution.

 

! We prompt the user for all the system parameters;

DATA:

  ARV_RATE = ?;

  SRV_TIME = ?;

  NO_SRVRS = ?;

ENDDATA

 

! The model;

! Average no. of busy servers;

  LOAD = ARV_RATE * SRV_TIME;

! Probability a given call must wait;

  PWAIT = @PEB( LOAD, NO_SRVRS);

! Conditional expected wait, i.e., given must wait;

  WAITCND = SRV_TIME/( NO_SRVRS - LOAD);

! Unconditional expected wait;

  WAITUNC = PWAIT * WAITCND;

END

Model: QMMC