Optimization of Traffic Control in MMAP[c]/PH[c]/S Catastrophic Queueing Model with PH Retrial Times and Controllable Preemptive Repeat Priority Policy

TL;DR

This paper develops a complex multi-server queueing model with preemptive priority policies for normal and catastrophic scenarios, incorporating PH distributed retrial times and optimizing backup channels using genetic algorithms.

Contribution

It introduces a novel queueing model with catastrophic and normal scenarios, including emergency call handling and backup channel optimization with NSGA-II.

Findings

Ergodicity criteria for the Markov chain are established.

Optimal backup channel numbers are obtained via NSGA-II.

Model effectively manages emergency and normal traffic scenarios.

Abstract

The presented study elaborates a multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type (PH) distributed retrial times. For the sake of comprehension, the scenario of model operation prior and later to the occurrence of the disaster is referred to as the normal scenario and as the catastrophic scenario, respectively. In the normal scenario, the incoming heterogeneous calls are categorized as handoff calls and new calls. Handoff calls are provided controllable preemptive priority over new calls. In the catastrophic scenario, when a disaster causes the shut down of the entire system and failure of all functioning channels, a set of backup channels is quickly deployed to restore services. Due to the emergency situation in the concerned area, the incoming heterogeneous calls are divided into three categories: handoff, new call, and emergency calls. Emergency calls are provided controllable preemptive priority over new/handoff calls due to the pressing need to save lives in such situations. The Markov chain's ergodicity criteria are established by demonstrating that it belongs to the class of asymptotically quasi-Toeplitz Markov chains (AQTMC). Further, a multi-objective optimization problem to obtain optimal number of backup channels has been formulated and dealt by employing non-dominated sorting genetic algorithm-II (NSGA-II) approach.