Optimization of traffic control in $ MMAP\mathit{[2]}/PH\mathit{[2]}/S$ priority queueing model with $ PH $ retrial times and the preemptive repeat policy

Abstract

The presented study elaborates a multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution (\begin{document}$ P\!H $\end{document}) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new calls. The arrival and service processes of both types of calls follow marked Markovian arrival process (\begin{document}$ M\!M\!A\!P $\end{document}) and \begin{document}$ P\!H $\end{document} distribution with distinct parameters, respectively. An arriving new call will be blocked when all the channels are occupied, and consequently will join the orbit (virtual space) to retry following \begin{document}$ P\!H $\end{document} distribution. When all the channels are occupied and a handoff call arrives at the system, out of the following two scenarios, one might take place. In the first scenario, if all the channels are occupied with handoff calls, the arriving handoff call will be lost from the system. While in the second one, if all the channels are occupied and at least one of them is serving a new call, the arriving handoff call will be provided service by using preemptive priority over that new call and the preempted new call will join the orbit. Behaviour of the proposed system is modelled by the level dependent quasi-birth-death \begin{document}$ (L\!D\!Q\!B\!D) $\end{document} process. The expressions of various performance measures have been derived for the numerical illustration. An optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.