PriMera Scientific Engineering (ISSN: 2834-2550)

Review Article

Volume 5 Issue 5

Control Theory for Queuing Systems with Moving Servers and Some Open Problems

Asaf Hajiyev*

October 30, 2024

DOI : 10.56831/PSEN-05-161

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Abstract

For queuing systems with moving servers, the control policy which means delays of a beginning service is introduced. In the capacity of efficiency index of systems is taken a customer’s average waiting time before service. Although it seems that it is a paradoxical idea to introduce delays of beginning service, it is shown that for some systems it gives a gain in a customer’s average waiting time before service. The class of queuing systems for which it is advisable to introduce delays is described. The form of an optimal function minimizing the efficiency index is found.

It is shown that if the intervals between neighbor services have exponential distribution, then the gain in a customer’s average waiting time before service equals 10% and independent of parameter of exponential distribution. For uniform distribution such gain equals 3.5% and also independent of parameter of uniform distribution. The criterion to define for which systems the gain is greater are given. Some open problems and numerical examples demonstrating theoretical results are given.

Keywords: queues with moving servers; a customer’s average waiting time; delay of beginning service; optimal function

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