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

TL;DR

This paper models and optimizes a complex multi-server queueing system with catastrophic failures, preemptive priorities, and retrial times, proposing new analytical and computational methods for system performance and backup channel optimization.

Contribution

It introduces a novel multi-server queueing model with PH retrial times and preemptive priority policies under catastrophic scenarios, including a new approach for stationary distribution computation and backup channel optimization.

Findings

Established ergodicity criteria for the Markov chain model.

Developed a new method for approximate stationary distribution calculation.

Optimized the number of backup channels using NSGA-II algorithm.

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 both scenarios, the arrival and service processes of all types of calls follow marked Markovian arrival process (MMAP) and PH distribution with distinct parameters, respectively. In the normal scenario, the incoming heterogeneous calls are categorized as handoff calls and new calls. An arriving new call will be blocked when all the channels are occupied, and consequently, will join the orbit (virtual space) of infinite capacity. From the orbit, the blocked new call can either retry for the service or exit the system following PH distribution. Whereas, an arriving handoff call is given preemptive repeat priority over a new call in service when all the channels are occupied and at least one of the channel is occupied with a new call otherwise the handoff call is dropped, and consequently, this preempted new call will join the orbit. 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. The Markov chain's ergodicity criteria are established by demonstrating that it belongs to the class of asymptotically quasi-Toeplitz Markov chains (AQTMC). For the approximate computation of the stationary distribution, a new approach is developed. An optimization problem to obtain optimal value of total number of backup channels has been formulated and dealt by employing non dominated sorting genetic algorithm-II (NSGA-II) approach.