Multi-Server Queueing Model with Broadcasting Service

The MAP/PH/N multi-server queuing system with broadcasting service discipline and server heating

“…Later, the disciplines at which a random number of servers can be needed for the customer ser vice appeared [1]. Recently, models wherein the arrived customer is served by all the servers that are free at the moment of the incoming have been introduced [2][3][4].…”

The SM/M/N queueing system with broadcasting service

“…Such a discipline suggests that if the arriving into the system customer meets several free servers upon arrival, all these servers start, independently of others, the service of this customer. Such a discipline is realistic, for example, in multiantenna communication networks The multiserver model of the MAP/PH/N type with the broadcasting service discipline was recently considered in [5]. In our present paper, we impose more strong assumptions about the service process (the class of PH phase-type distributions is much more rich than the set of exponential distributions considered in the present paper), but the arrival process of SM type, considered in this paper, is an essentially more wide class than the set of the Markovian arrival processes.…”

“…In our present paper, we impose more strong assumptions about the service process (the class of PH phase-type distributions is much more rich than the set of exponential distributions considered in the present paper), but the arrival process of SM type, considered in this paper, is an essentially more wide class than the set of the Markovian arrival processes. So, the model considered in [5] could be exploited for performance evaluation and capacity planning in real-life systems in situations when the service time distribution cannot be well approximated by the exponential distribution. While the present model allows to consider more complicated arrival processes, it is worth to mention that, except our paper [5], the model studied in this paper was not previously investigated in the literature even in the much simpler case of the stationary Poisson arrival process and exponential service time distribution.…”

“…So, the model considered in [5] could be exploited for performance evaluation and capacity planning in real-life systems in situations when the service time distribution cannot be well approximated by the exponential distribution. While the present model allows to consider more complicated arrival processes, it is worth to mention that, except our paper [5], the model studied in this paper was not previously investigated in the literature even in the much simpler case of the stationary Poisson arrival process and exponential service time distribution.…”

“…Due to the different assumptions about the input flow and service process, analysis of the stochastic processes in the model in this paper and the model in [5] is quite different. In [5], the multidimensional continuous time Markov chain is under study. Here we have to analyze first the two-dimensional discrete time Markov chain embedded at the epochs of the customers arrival into the system.…”