Study and Simulation of Queuing Theory in the Toll Motorway

HoudaMehri * Taou?kDjemel—**

*Research Unit in Logistics, Industrial Management and Quality

(LOGIQ) - ISGI-Sfax. BP nr?954-3018 Sfax-TUNISIA.

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** GIAD Laboratory, University of Sfax, FSEG,

Route de lŠAerodrome, km 4, BP 1088, 3018 Sfax, Tunisia .

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QT 14

ABSTRACT.

Adjustment tests in a case study show that arrival times and service times in a motorway queuing system led to the model M/Γ(α,β)/c.

There are no analytical formula to calculate performance measures of such a model. In this article, we generalize PollazeckKhitchinne’s formula to establish approximate formula of these measures and we present a simulator that calculates performance measures of A/B/c queuing system where A,B can be one of the following distributions: determinist, exponential, Erlang or Gamma.

We verify the theory according to which the type of organization of the queue (an unique queue for all the servers or multiple queues where each server has his/her own queue) does not in?uence the performance measures of the queuing system.

KEYWORDS:

Queues, statistical analysis, multi agent simulation, exponential distribution, Gamma distribution.