Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations

This paper deals with an M/G/1 queue with multiple optional services and multiple optional vacations for an unreliable server queue. All arriving customers require a First Essential Service (FES), while only some of them ask for other optional services. The stability and ergodicity condition for the model has been discussed. By introducing supplementary variables and employing the generating function technique, we derive the system size distribution at the random epoch as well as the departure epoch. Waiting time distribution and some other queuing and reliability measures have also been obtained. The sensitivity analysis has been facilitated by taking numerical illustrations to explore the effect of the different parameters on various performance indices.

[1]  Adhir K Basu,et al.  Introduction to Stochastic Process , 2002 .

[2]  Jinting Wang,et al.  An M/G/1 queue with second optional service and server breakdowns , 2004 .

[3]  Kuo-Hsiung Wang,et al.  A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity , 2000 .

[4]  Antoine-S Bailly,et al.  Science régionale - Walter Isard, Introduction to régional science. Englewood Cliffs (NJ), Prentice-Hall, 1975 , 1975 .

[5]  Kuo-Hsiung Wang,et al.  A maximum entropy approach for the (p,N)-policy M/G/1 queue with a removable and unreliable server , 2009 .

[6]  Madhu Jain,et al.  Optimal repairable M x /G/1 queue with multi-optional services and Bernoulli vacation , 2010 .

[7]  V. Thangaraj,et al.  A Single Server M/G/1 Feedback Queue with Two Types of Service Having General Distribution , 2010 .

[8]  Madhu Jain,et al.  Optimal policy for bulk queue with multiple types of server breakdown , 2009 .

[9]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[10]  Zaiming Liu,et al.  On the BMAP/G/1 G-queues with second optional service and multiple vacations , 2009 .

[11]  Stefanka Chukova,et al.  Single-server Poisson queueing system with splitting and delayed-feedback: Part I , 2011, Int. J. Math. Oper. Res..

[12]  Jau-Chuan Ke,et al.  Batch arrival queues under vacation policies with server breakdowns and startup/closedown times , 2007 .

[13]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[14]  Avishai Mandelbaum,et al.  Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime , 2008, Math. Oper. Res..

[15]  Anamika Jain,et al.  Working vacations queueing model with multiple types of server breakdowns , 2010 .

[16]  P. Vijaya Laxmi,et al.  Renewal input infinite buffer batch service queue with single exponential working vacation and accessibility to batches , 2011, Int. J. Math. Oper. Res..

[17]  Linn I. Sennott,et al.  Technical Note - Mean Drifts and the Non-Ergodicity of Markov Chains , 1983, Oper. Res..

[18]  Gautam Choudhury,et al.  An M/G/1 queue with an optional second vacation , 2006 .

[19]  Bin Liu,et al.  Transient analysis of an M , 2008, Eur. J. Oper. Res..

[20]  Gautam Choudhury,et al.  An M/G/1 retrial queueing system with two phases of service subject to the server breakdown and repair , 2008, Perform. Evaluation.

[21]  M. Haridass,et al.  Analysis of a Bulk Queue with Unreliable Server and Single Vacation , 2008 .

[22]  K. H. Wang,et al.  (Applied Mathematical Modelling,33(4):2024-2034)A Maximum Entropy Approach for the -Policy M/G/1 Queue with a Removable and Unreliable Server , 2009 .

[23]  B. Krishna Kumar,et al.  An M/M/2 queueing system with heterogeneous servers and multiple vacations , 2005, Math. Comput. Model..

[24]  Jau-Chuan Ke,et al.  Batch arrival queue with N-policy and at most J vacations , 2010 .

[25]  Jau-Chuan Ke,et al.  On a batch retrial model with J vacations , 2009, J. Comput. Appl. Math..

[26]  R.a c Arumuganathan,et al.  Analysis of a bulk queue with multiple vacations and closedown times , 2004 .

[27]  Xian Zhou,et al.  Stochastic Scheduling Subject to Preemptive-Repeat Breakdowns with Incomplete Information , 2009, Oper. Res..

[28]  Gautam Choudhury,et al.  An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair , 2009 .

[29]  J. G. Dai,et al.  Customer Abandonment in Many-Server Queues , 2010, Math. Oper. Res..

[30]  Yutaka Takahashi,et al.  Queueing analysis: A foundation of performance evaluation, volume 1: Vacation and priority systems, Part 1: by H. Takagi. Elsevier Science Publishers, Amsterdam, The Netherlands, April 1991. ISBN: 0-444-88910-8 , 1993 .

[31]  Kailash C. Madan,et al.  An M/G/1 queue with second optional service , 1999, Queueing Syst. Theory Appl..

[32]  Quanlin Li,et al.  Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs , 2001, Queueing Syst. Theory Appl..

[33]  M. Haridass,et al.  Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs , 2011, Int. J. Math. Oper. Res..

[34]  Jesús R. Artalejo,et al.  Steady State Analysis of an M/G/1 Queue with Repeated Attempts and Two-Phase Service , 2004 .

[35]  Jesús R. Artalejo,et al.  New results in retrial queueing systems with breakdown of the servers , 1994 .

[36]  David Frankel,et al.  brief review: Queueing Analysis: A Foundation of Performance Evaluation. Volume 1: Vacation and Priority Systems, Part 1 by H. Takagi (North-Holland, 1991) , 1991, PERV.