The M/M/1 retrial queue with retrials due to server failures
- 163 Downloads
Sherman and Kharoufeh (Oper. Res. Lett. 34:697–705, ) considered an M/M/1 type queueing system with unreliable server and retrials. In this model it is assumed that if the server fails during service of a customer, the customer leaves the server, joins a retrial group and in random intervals repeats attempts to get service. We suggest an alternative method for analysis of the Markov process, which describes the functioning of the system, and find the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial group in steady state.
KeywordsRetrials Unreliable server Steady state
Mathematics Subject Classification (2000)60K25 90B22
Unable to display preview. Download preview PDF.
- 2.Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman and Hall, London (1997) Google Scholar
- 3.Sherman, N.P., Kharoufeh, J.P., Abramson, M.: An M/G/1 retrial queue with unreliable server for streaming multimedia applications. Probab. Eng. Inf. Sci. (in press) Google Scholar
- 4.Tweedie, R.L.: Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. In: Math. Proceedings of the Cambridge Philosophical Society, vol. 78, part 1 (1975) Google Scholar
- 5.Malyshev, M.V., Menshikov, M.V.: Ergodicity, continuity and analyticity of countable Markov chains. In: Proceedings of the Moscow Math. Society, vol. 39 (1979) Google Scholar