Analysis of a nonpreemptive priority queue with exponential timer and server vacations

We consider multi-class priority queues with nonpreemptive services controlled by an exponential timer and multiple vacations. By reducing this model to the priority model with Bernoulli schedule analyzed by Katayama (1997), we obtain the Laplace-Stieltjes transform for the sojourn time in the system for each priority class, assuming (i) constant service times or (ii) general service times with either 1-limited or exhaustive service, and provide recursive equations to evaluate its first two moments.

[1]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[2]  Hideaki Takagi,et al.  Stochastic Analysis of Computer and Communication Systems , 1990 .

[3]  Tsuyoshi Katayama,et al.  System delay analysis for a nonpreemptive time-limited service queueing system with two types of vacations and its application , 2003 .

[4]  Onno J. Boxma,et al.  Workloads and waiting times in single-server systems with multiple customer classes , 1989, Queueing Syst. Theory Appl..

[5]  T. Katayama,et al.  Two-class priority queueing system with time-limited schedule , 1997, PMCCN.

[6]  Kin K. Leung,et al.  Two Vacation Models for Token-Ring Networks where Service is Controlled by Timers , 1994, Perform. Evaluation.

[7]  Kyung C. Chae,et al.  An Arrival Time Approach to M/G/1-type Queues with Generalized Vacations , 2001, Queueing Syst. Theory Appl..

[8]  R. Lehnert,et al.  Providing Quality of Service in Heterogeneous Environments , 2003 .

[9]  Kin K. Leung,et al.  A Single-Server Queue with Vacations and Non-Gated Time-Limited Service , 1991, Perform. Evaluation.

[10]  Tsuyoshi Katayama,et al.  Priority queues with Bernoulli schedules , 1997 .

[11]  Toshiharu Hasegawa,et al.  Performance and Management of Complex Communication Networks , 1998, IFIP — The International Federation for Information Processing.

[12]  Offer Kella,et al.  Priorities in M/G/1 queue with server vacations , 1988 .

[13]  Yoshitaka Takahashi,et al.  ANALYSIS OF A TWO-CLASS PRIORITY QUEUE WITH BERNOULLI SCHEDULES , 1992 .

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

[15]  Tsuyoshi Katayama.  Level-crossing approach to a time-limited service system with two types of vacations , 2005, Oper. Res. Lett..

[16]  Edward G. Coffman,et al.  Two Queues with Alternating Service Periods , 1987, Performance.

[17]  Gadi Fibich,et al.  A Communication Multiplexer Problem: Two Alternating Queues with Dependent Randomly-Timed Gated Regime , 2002, Queueing Syst. Theory Appl..

[18]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[19]  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 .

[20]  Robert D. van der Mei,et al.  Waiting times in a two-queue model with exhaustive and Bernoulli service , 1994, Math. Methods Oper. Res..

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

[22]  Tsuyoshi Katayama,et al.  Analysis and Evaluation of Packet Delay Variance in the Internet , 2002 .

[23]  Lajos Takács,et al.  Priority queues , 2019, The Art of Multiprocessor Programming.

[24]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .