Resource optimization in $\textit{MMAP[2]/PH[2]/S}$ priority queueing model with threshold $\textit{PH}$ retrial times and the preemptive resume policy

Abstract

The findings of this article expounds a multi-server priority queueing model by taking into account the preemptive resume priority scheduling and threshold based phase-type distribution ($P\!H\!D$) for retrial process. On the basis of priority, the incoming heterogeneous traffic is categorized as high priority traffic ($H\!P\!T$) and low priority traffic ($L\!P\!T$). When all the channels are busy, an arriving $L\!P\!T$ will be denied for the service, and it will enter the orbit (virtual space) to retry after some time. The retrial process will follow $P\!H\!D$ when the number of $L\!P\!T$ is less than some threshold value otherwise the retrial process will follow exponential distribution. One of the following two instances may occur when all of the channels are occupied and a $H\!P\!T$ enters the system. In the first instance, the arriving $H\!P\!T$ will be discarded from the system if all the channels are packed with $H\!P\!T$ solely. On the contrary, in the second instance, the approaching $H\!P\!T$ will be provided service by employing preemptive priority when at least one $L\!P\!T$ is receiving service, and that preempted $L\!P\!T$ will enter a buffer of finite capacity. Whenever an idle channel is found, the preempted $L\!P\!T$ will begin its service from the termination phase. The level dependent quasi-birth-death process is used for the modeling and analysis of the proposed framework. By establishing that the proposed Markov chain satisfies the asymptotically quasi-Toeplitz Markov chain classification, the ergodicity conditions for the chain are demonstrated. For the numerical illustration, the expressions of several performance measures have been developed. The non-dominated sorting genetic algorithm-II approach has been used to address an optimization problem for resource optimization and traffic control.