Analysis of a GI/M/1 queue in a multi-phase service environment with disasters

In this paper, we study a single server GI/M/1 queue in a multi-phase service environment with disasters, where the disasters occur only when the server is busy serving customers. Whenever a disaster occurs in an operative service phase, all present customers are forced to leave the system simultaneously, the server abandons the service and an exponential repair time is set on. After the system is repaired, the server resumes his service and moves to service phase i immediately with probability q i ,i = 1,2, ... ,N . Using the matrix analytic approach and semi-Markov process, we obtain the stationary queue length distribution at both arrival and arbitrary epochs. After introducing tagged customers and the concept of a cycle, we also derive the sojourn time distribution, the duration of a cycle, and the length of the server’s working time in a service cycle. In addition, numerical examples are presented to illustrate the impact of some critical model parameters on performance measures.

[1]  Li Tao,et al.  The GI/M/1 queue with Bernoulli-schedule-controlled vacation and vacation interruption , 2013 .

[2]  Srinivas R. Chakravarthy.  A disaster queue with Markovian arrivals and impatient customers , 2009, Appl. Math. Comput..

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

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

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

[6]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[7]  Antonis Economou,et al.  Equilibrium balking strategies for a clearing queueing system in alternating environment , 2013, Ann. Oper. Res..

[8]  Michael A. Zazanis,et al.  An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy , 2015 .

[9]  Uri Yechiali,et al.  An M/M/1 Queue in Random Environment with disasters , 2014, Asia Pac. J. Oper. Res..

[10]  Doo Ho Lee,et al.  The M/G/1 queue with disasters and working breakdowns , 2014 .

[11]  Naishuo Tian,et al.  Performance analysis of a GI/M/1 queue with single working vacation , 2011, Appl. Math. Comput..

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

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

[14]  Antonis Economou,et al.  Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes , 2012, Eur. J. Oper. Res..

[15]  Antonis Economou,et al.  The Single Server Queue with Catastrophes and Geometric Reneging , 2013 .

[16]  Won S. Yang,et al.  Analysis of the GI/Geo/1 Queue with Disasters , 2009 .

[17]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

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

[19]  Ivan Atencia,et al.  The discrete-time Geo/Geo/1 queue with negative customers and disasters , 2004, Comput. Oper. Res..

[20]  Antonis Economou,et al.  The effect of catastrophes on the strategic customer behavior in queueing systems , 2013 .

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

[22]  Liwei Liu,et al.  Analysis of the M/G/1 queue in multi-phase random environment with disasters , 2015 .

[23]  Won Seok Yang,et al.  The N-policy of a discrete time Geo/G/1 queue with disasters and its application to wireless sensor networks , 2013 .