$$M/D^{[y]}/1$$M/D[y]/1 Periodically gated vacation model and its application to IEEE 802.16 network

In this paper we consider the analysis of an $$M/D^{[y]}/1$$M/D[y]/1 vacation queue with periodically gated discipline. The motivation of introducing the new periodically gated discipline lies in modeling a kind of contention-based bandwidth reservation mechanism applied in wireless networks. The analysis approach applied here consists of two steps and it is based on appropriately chosen characteristic epochs of the system. We provide approximate expressions for the probability-generating function of the number of customers at arbitrary epoch as well as for the Laplace–Stieljes transform and for the mean of the steady-state waiting time. Several numerical examples are also provided. In the second part of the paper we discuss how to apply the periodically gated vacation model to the non real-time uplink traffic in IEEE 802.16-based wireless broadband networks.

[1]  N. K. Jaiswal,et al.  A Bulk‐Service Queueing Problem with Variable Capacity , 1961 .

[2]  Kyung-Chul Chae,et al.  A fixed-size batch service queue with vacations , 1996 .

[3]  Wuyi Yue,et al.  Advances in Queueing Theory and Network Applications , 2009 .

[4]  R. Anitha,et al.  Bulk service non-Markovian queues with exceptional first vacation , 1999 .

[5]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[6]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[7]  Sergey D. Andreev,et al.  Delay Analysis of Wireless Broadband Networks with Non Real-Time Traffic , 2011, MACOM.

[8]  Lida Thomo.  A multiple vacation model M x G 1 with balking , 1997 .

[9]  Mohan L. Chaudhry,et al.  Numerical analysis for bulk-arrival queueing systems: Root-finding and steady-state probabilities inGIr/M/1 queues , 1987 .

[10]  Hideaki Takagi,et al.  M/G/1 queue with multiple working vacations , 2006, Perform. Evaluation.

[11]  Miklós Telek,et al.  M/G/1 Queue with Exponential Working Vacation and Gated Service , 2011, ASMTA.

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

[13]  Mohan L. Chaudhry,et al.  Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues , 1987, Queueing Syst. Theory Appl..

[14]  Sem C. Borst,et al.  Polling Models With and Without Switchover Times , 1997, Oper. Res..

[15]  U. C. Gupta,et al.  Analytic and numerical aspects of batch service queues with single vacation , 2005, Comput. Oper. Res..

[16]  Sergey D. Andreev,et al.  Analysis of Periodically Gated Vacation Model and Its Application to IEEE 802.16 Network , 2012, ASMTA.

[17]  Norman T. J. Bailey,et al.  On Queueing Processes with Bulk Service , 1954 .

[18]  Naishuo Tian,et al.  Vacation Queueing Models Theory and Applications , 2006 .

[19]  Wuyi Yue,et al.  Analysis of multi-server queue with synchronous vacations and gated discipline , 2011, QTNA.

[20]  Jewgeni H. Dshalalow,et al.  Bulk input queues with quorum and multiple vacations , 1996 .

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

[22]  T. DoshiB..  Queueing systems with vacationsa survey , 1986 .

[23]  Vidyadhar G. Kulkarni,et al.  Explicit solutions for the steady state distributions in M/PH/1 queues with workload dependent balking , 2006, Queueing Syst. Theory Appl..

[24]  Leslie D. Servi,et al.  M/M/1 queues with working vacations (M/M/1/WV) , 2002, Perform. Evaluation.

[25]  Sergey D. Andreev,et al.  Upper Bound on Overall Delay in Wireless Broadband Networks with Non Real-Time Traffic , 2010, ASMTA.

[26]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..