Analysis and optimization of Guard Channel Policy in cellular mobile networks with account of retrials

A multi-server retrial queue with two types of calls (handover and new calls) is analyzed. This queue models the operation of a cell of a mobile communication network. Calls of two types arrive at the system according to the Marked Markovian Arrival Process. Service times of both types of the calls are exponentially distributed with different service rates. Handover calls have priority over new calls. Priority is provided by means of reservation of several servers of the system exclusively for service of handover calls. A handover call is dropped and leaves the system if all servers are busy at the arrival epoch. A new call is blocked if all servers available to new calls are busy. Such a call has options to balk (to leave the system without getting the service) or to retry later on. The behavior of the system is described by the four-dimensional Markov chain belonging to the class of the asymptotically quasi-Toeplitz Markov chains (AQTMC). In the paper, a constructive ergodicity condition for this chain is derived and the effective algorithm for computing the stationary distribution is presented. Based on this distribution, formulas for various performance measures of the system are obtained. Results of numerical experiments illustrating the behavior of key performance measures of the system depending on the number of the reserved servers under the different shares of the handover and the new calls are presented. An optimization problem is considered and high positive effect of server's reservation is demonstrated.

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