Cost analysis of a MAP/PH/S performability model with PH retrial times using simulated annealing method.

This work focuses over the performability analysis of a multi-server retrial queueing model with phase-type inter-retrial times in cellular networks. It is considered that the pattern of the new call arrival and handoff call arrival follows Markovian arrival process (MAP). The service times of both types of calls are phase-type (PH ) distributed with different service rates, and inter-failure & inter-repair times of channels are exponentially distributed. For the prioritization of handoff calls, G channels are kept in reserve for handoff calls. When all the available channels, say S, are busy at the arrival epoch of a handoff call, the handoff call will be dropped. Whereas a new call will be blocked and will have an option to join the orbit of infinite capacity or leave the system without getting the connection, if at least S-G channels are busy. A new call in the orbit, termed as retrial call, retries to get the connection after a random interval which follows PH distribution. This model is analyzed as a level-dependent-quasi-birth-death (LDQBD) process by applying matrix-analytic method (MAM). Further, the closed-form expressions for essential performance measures of the proposed model are derived. Through numerical illustrations, the behaviour of performance measures depending on the various relevant intensities is discussed. An expected cost optimization problem is formulated to determine the optimal value of service intensity and the optimal value of repair intensity. The cost function analysis is executed by employing Simulated Annealing (SA) method.