Investigation of the BMAP/G/1--> super(./)PH1/M tandem queue with retrials and losses

• Published in: Applied mathematical modelling 2010-10, Vol.34 (10), p.2926-2940
• Main Authors: Kim, Che Soong, Park, Seog Ha, Dudin, Alexander, Klimenok, Valentina, Tsarenkov, Gennady
• Format: Article
• Language: English
• Subjects: Arrivals; Communication systems; Customers; Indexing in process; Mathematical analysis; Mathematical models; Queues
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2010.01.003

Tandem queues are good models for different fragments of communication systems and networks, so their investigation is interesting for theory and applications. Retrial tandem queues did not get enough attention in literature. In the present paper, the analytic analysis of tandem retrial queue is implemented under general assumptions about the system parameters. Possible correlation and group arrivals are taken into account by means of considering the Batch Markovian Arrival Process (BMAP) as input stream to the system. The service time at the first phase is assumed to be generally distributed and be different for primary and repeated customers. The service time distribution at the second phase is assumed to be of PH (PHase) type. General assumptions about the form of the total retrial intensity are made. The loss of customers, which meet the second phase of the system be full at the service completion at the first phase, is assumed. Markov chain embedded at service completion epochs at the first service phase and the process of system states at arbitrary time are investigated. Probability of immediate access to the first phase of the service and probability of a loss at the second stage are calculated. Numerical illustrations are presented. They illustrate the feasibility of the proposed algorithms and importance of exact account of a nature of the arrival and service processes.