The M/G/1 queue with disasters and working breakdowns

Abstract In this paper, we analyze the M/G/1 queueing system with disasters and working breakdown services. The system consists of a main server and a substitute server, and disasters only occur while the main server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair shop and the repair period immediately begins. During the repair period, the system is equipped with the substitute server which provides the working breakdown services to arriving customers. After introducing the concept of working breakdown services, we derive the system size distribution and the sojourn time distribution. We also obtain the results of the cycle analysis. In addition, numerical works are given to examine the relation between the sojourn time and the some system parameters.

[1]  Satish K. Tripathi,et al.  A single server priority queue with server failures and queue flushing , 1989, Oper. Res. Lett..

[2]  Karl Sigman,et al.  A Pollaczek–Khintchine formula for M/G/1 queues with disasters , 1996, Journal of Applied Probability.

[3]  Won S. Yang,et al.  A note on the GI/M/1 queue with Poisson negative arrivals , 2001, Journal of Applied Probability.

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

[5]  B. Avi-Itzhak,et al.  A Many-Server Queue with Service Interruptions , 1968, Oper. Res..

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

[7]  Uri Yechiali,et al.  Queues with system disasters and impatient customers when system is down , 2007, Queueing Syst. Theory Appl..

[8]  Hendrik Baumann,et al.  Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes , 2012, Comput. Oper. Res..

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

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

[11]  Eric Renshaw,et al.  The M / M /1 queue with mass exodus and mass arrivals when empty , 1997 .

[12]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[13]  Antonis Economou,et al.  Synchronized abandonments in a single server unreliable queue , 2010, Eur. J. Oper. Res..

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

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

[16]  J. Gani,et al.  Birth, immigration and catastrophe processes , 1982, Advances in Applied Probability.

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

[18]  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..

[19]  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..

[20]  Jesús R. Artalejo,et al.  Analysis of a stochastic clearing system with repeated attempts , 1998 .

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

[22]  Jau-Chuan Ke,et al.  An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server , 2006, Math. Methods Oper. Res..

[23]  Won S. Yang,et al.  ANALYSIS OF M/G/1 STOCHASTIC CLEARING SYSTEMS , 2002 .

[24]  R. Sudhesh.  Transient analysis of a queue with system disasters and customer impatience , 2010, Queueing Syst. Theory Appl..

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