On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

Ali Delavarkhalafi

doi:10.3934/naco.2021030

Article Contents

2022, Volume 12, Issue 4: 693-703. Doi: 10.3934/naco.2021030

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On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

Ali Delavarkhalafi

Mathematical Sciences Department, Yazd University, Yazd, Iran

Received: November 30, 2020

Revised: May 31, 2021

Early access: August 2021

Published: December 2022

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Abstract

In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate $ \lambda(t) $ and exponential service processes with $ \mu $ rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.

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Mathematics Subject Classification: Primary: 93E20, 35R60; Secondary: 60K20.

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Figure 1. Variations of non linear function over u

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