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

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 ( $$P\!H\!D$$ P H D ) for retrial process. On the basis of priority, the incoming heterogeneous traffic is categorized as high priority traffic ( $$H\!P\!T$$ H P T ) and low priority traffic ( $$L\!P\!T$$ L P T ). When all the channels are busy, an arriving $$L\!P\!T$$ 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 $$P\!H\!D$$ P H D when the number of $$L\!P\!T$$ 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 $$H\!P\!T$$ H P T enters the system. In the first instance, the arriving $$H\!P\!T$$ H P T will be discarded from the system if all the channels are packed with $$H\!P\!T$$ H P T solely. On the contrary, in the second instance, the approaching $$H\!P\!T$$ H P T will be provided service by employing preemptive priority when at least one $$L\!P\!T$$ L P T is receiving service, and that preempted $$L\!P\!T$$ L P T will enter a buffer of finite capacity. Whenever an idle channel is found, the preempted $$L\!P\!T$$ 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.