Performability analysis of a MMAP[2]/PH[2]/S model with PH retrial times

Abstract

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 marked Markovian arrival process. The service times of both types of calls are phase-type (PH) distributed with different parameters, 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 process by applying an efficient method. Through numerical illustrations, the behavior of performance measures depending on the various relevant intensities is discussed.

Keywords:

• Channel failure
• LDQBD process
• Markovian arrival process
• performability model
• phase-type distribution
• retrial queue

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Additional information

Funding

The second author, Raina Raj is supported by a senior research fellowship (SRF) grant No.-09/1131(0024)/2018-EMR-I from Council of Scientific and Industrial Research (CSIR), India.