Analysis of the M/G/1 processor-sharing queue with bulk arrivals

We analyze the single server processor-sharing queue for the case of bulk arrivals. We obtain an expression for the expected response time of a job as a function of its size, when the service times of jobs have a generalized hyperexponential distribution and more generally for distributions with rational Laplace transforms. Our analysis significantly extends the class of distributions for which processor-sharing queues with bulk arrivals were previously analyzed.

[1]  William G. Marchal,et al.  Distribution Estimation Using Laplace Transforms , 1998, INFORMS J. Comput..

[2]  R. Schassberger,et al.  A new approach to the M/G/1 processor-sharing queue , 1984, Advances in Applied Probability.

[3]  Kiran M. Rege,et al.  Response Time Distribution in a Multiprogrammed Computer with Terminal Traffic , 1988, Perform. Evaluation.

[4]  Bhaskar Sengupta,et al.  A Functional Equation Arising in a Queue With a Gating Mechanism , 1989, Probability in the Engineering and Informational Sciences.

[5]  A. Bobbio,et al.  A benchmark for ph estimation algorithms: results for acyclic-ph , 1994 .

[6]  Kiran M. Rege,et al.  The M/G/1 Processor-Sharing Queue with Bulk Arrivals , 1993, Modelling and Evaluation of ATM Networks.

[7]  S. F. Yashkov,et al.  Processor-sharing queues: Some progress in analysis , 1987, Queueing Syst. Theory Appl..

[8]  KleinrockLeonard.  Time-shared Systems , 1967 .

[9]  Leonard Kleinrock,et al.  The processor-sharing queueing model for time-shared systems with bulk arrivals , 1971, Networks.

[10]  D. Cox.  A use of complex probabilities in the theory of stochastic processes , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Jingwen Li,et al.  An Approximation Method for the Analysis of GI/G/1 Queues , 1997, Oper. Res..

[12]  Carl M. Harris,et al.  Approximation with generalized hyperexponential distributions: Weak convergence results , 1986, Queueing Syst. Theory Appl..

[13]  T. Ott.  THE SOJOURN-TIME DISTRIBUTION IN THE M/G/1 QUEUE , 1984 .

[14]  Leonard Kleinrock,et al.  Time-shared Systems: a theoretical treatment , 1967, JACM.

[15]  A. P. Zwart,et al.  Sojourn time asymptotics in the M/G/1 processor sharing queue , 1998, Queueing Syst. Theory Appl..

[16]  R. Núñez-Queija.  SOJOURN TIMES IN NON-HOMOGENEOUS QBD PROCESSES WITH PROCESSOR SHARING , 2001 .

[17]  S. Grishechkin.  On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes , 1992, Advances in Applied Probability.