An M X /G/1 unreliable retrial queue with two phase service and persistence behaviour of customers in service
RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 1, pp. 9-32.

This paper describes an unreliable server batch arrival retrial queue with two types of repair and second optional service. The server provides preliminary first essential service (FES) to the primary arriving customers or customers from retrial group. On successful completion of FES, the customer may opt for second optional service (SOS) with probability α. The server is subject to active break downs. The customer under FES (or SOS) during the failure decides, with probability q, to join the orbit(impatientcustomer) and, with complementary probability p, to remain in the server for repair in order to conclude his remaining service (patientcustomer). Both service and repair times are assumed to have general distribution. It is considered that the repair time of server during the presence of patient customer and the repair time of the server while the customer (impatientcustomer) joining the orbit due to failure, are different. For this queueing system, the orbit and system size distributions are obtained. Reliability of the proposed model is analysed. Some particular cases are also discussed. Other performance measures are also obtained. The effects of several parameters on the system are analysed numerically.

DOI : 10.1051/ro/2012024
Classification : 60K25, 90B22
Mots-clés : first essential service, reliability measures, second optional service, unreliable server, persistent customers 
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     author = {Senthil Kumar, M. and Arumuganathan, R.},
     title = {An $M^{X}/G/1$ unreliable retrial queue with two phase service and persistence behaviour of customers in service},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {9--32},
     publisher = {EDP-Sciences},
     volume = {47},
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     zbl = {1273.60111},
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Senthil Kumar, M.; Arumuganathan, R. An $M^{X}/G/1$ unreliable retrial queue with two phase service and persistence behaviour of customers in service. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 1, pp. 9-32. doi : 10.1051/ro/2012024. http://www.numdam.org/articles/10.1051/ro/2012024/

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