Mean Waiting Times in Nonpreemptive Priority Queues with Markovian Arrival and i.i.d. Service Processes

Abstract This paper considers nonpreemptive priority queues with P (>=2) classes of customers. Customers in each class arrive to the system according to a Markovian Arrival Process (MAP). MAP is a class of non-renewal arrival processes and includes the Markov Modulated Poisson Process (MMPP). The service times of customers in all classes are independent and identically distributed according to a common distribution function. Using both generating function techniques and matrix analytic methods, we derive the mean waiting time for each customer class. The algorithmic implementation of the analytical results is also discussed along with numerical examples.

[1]  P. Jacobs,et al.  Finite Markov chain models skip-free in one direction , 1984 .

[2]  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 .

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

[4]  Tetsuya Takine,et al.  The workload in the MAP/G/1 queue with state-dependent services: its application to a queue with preemptive resume priority , 1994 .

[5]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[6]  M. Neuts,et al.  A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[7]  John Cosmas,et al.  Characterization of Video Codecs as Autoregressive Moving Average Processes and Related Queueing System Performance , 1991, IEEE J. Sel. Areas Commun..

[8]  Marcel F. Neuts,et al.  Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[9]  Tatsuya Suda,et al.  Survey of traffic control schemes and protocols in ATM networks , 1991, Proc. IEEE.

[10]  V. Ramaswami.  A stable recursion for the steady state vector in markov chains of m/g/1 type , 1988 .

[11]  Moshe Sidi,et al.  Discrete-time priority queueing systems with two-state Markov modulated arrival processes , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

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

[13]  Bernd Meister,et al.  Service in a Loop System , 1972, JACM.

[14]  David M. Lucantoni,et al.  A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance , 1986, IEEE J. Sel. Areas Commun..

[15]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .

[16]  Tetsuya Takine,et al.  Analysis of a Nonpreemptive Priority Queue with SPP Arrivals of High Class , 1995, Perform. Evaluation.

[17]  Tetsuya Takine,et al.  An analysis of a discrete-time queue for broadband ISDN with priorities among traffic classes , 1994, IEEE Trans. Commun..

[18]  Levent Gun,et al.  Experimental results on matrix-analytical solution techniques–extensions and comparisons , 1989 .