Analysis of MAP/M/1 queue with working breakdowns

ABSTRACT In this paper, we analyze the MAP/M/1 queue with working breakdowns. The number of customers in the system in the steady state is obtained by the matrix geometric solution method. Then, several useful performance measures are provided. Furthermore, we show a recursive formula to obtain an approximation of stationary sojourn time. At last, we present several numerical examples.

[1]  Ioannis Dimitriou,et al.  A repairable queueing model with two-phase service, start-up times and retrial customers , 2010, Comput. Oper. Res..

[2]  Tetsuya Takine,et al.  Sojourn time distribution in a MAP/M/1 processor-sharing queue , 2003, Oper. Res. Lett..

[3]  Igor N. Kovalenko,et al.  Introduction to Queuing Theory , 1989 .

[4]  Jau-Chuan Ke,et al.  Modified T vacation policy for an M/G/1 queueing system with an unreliable server and startup , 2005, Math. Comput. Model..

[5]  Gautam Choudhury,et al.  The optimal control of an Mx/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule , 2011, Math. Comput. Model..

[6]  Gennadi Falin.  An M/G/1 retrial queue with an unreliable server and general repair times , 2010, Perform. Evaluation.

[7]  Gautam Choudhury,et al.  A BATCH ARRIVAL RETRIAL QUEUE WITH GENERAL RETRIAL TIMES UNDER BERNOULLI VACATION SCHEDULE FOR UNRELIABLE SERVER AND DELAYING REPAIR , 2012 .

[8]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[9]  Peter W. Glynn,et al.  Computing Poisson probabilities , 1988, CACM.

[10]  W. D. Ray,et al.  Stochastic Models: An Algorithmic Approach , 1995 .

[11]  V. Ramaswami,et al.  Advances in Probability Theory and Stochastic Processes , 2001 .

[12]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[13]  Ramanath Kasturi,et al.  A queue with working breakdowns , 2012, Comput. Ind. Eng..

[14]  P. Naor,et al.  Some Queuing Problems with the Service Station Subject to Breakdown , 1963 .

[15]  Marcel F. Neuts.  Models Based on the Markovian Arrival Process , 1992 .

[16]  B. V. Gnedenko,et al.  Introduction to queueing theory (2nd ed) , 1989 .

[17]  Ioannis Dimitriou,et al.  A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers , 2013 .

[18]  Qi-Ming He,et al.  Fundamentals of Matrix-Analytic Methods , 2013, Springer New York.

[19]  Zhe George Zhang,et al.  Optimal (d, c) vacation policy for a finite buffer M/M/c queue with unreliable servers and repairs , 2009 .

[20]  Jau-Chuan Ke,et al.  Bi-level control for batch arrival queues with an early startup and un-reliable server , 2004 .

[21]  V. Sridharan,et al.  Some characteristics on a finite queue with normal partial and total failures , 1996 .

[22]  MELIKE BAYKAL-GURSOY,et al.  Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates , 2004, Queueing Syst. Theory Appl..

[23]  Srinivas R. Chakravarthy.  The Batch Markovian Arrival Process: A Review and Future Work , 2001 .

[24]  Jau-Chuan Ke,et al.  On M/G/1 system under NT policies with breakdowns, startup and closedown , 2006 .

[25]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[26]  Xiuli Chao,et al.  Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations , 1997, Journal of Applied Probability.

[27]  Won Seok Yang,et al.  Geo/G/1 queues with disasters and general repair times , 2011 .