Product form in networks of queues with batch arrivals and batch services

A product form equilibrium distribution is derived for a class of queueing networks in either discrete or continuous time, in which multiple customers arrive simultaneously and batches of customers complete service simultaneously.

[1]  Peter G. Taylor,et al.  A net level performance analysis of stochastic Petri nets , 1989, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[2]  W. Henderson,et al.  Insensitivity of processes with interruptions , 1989, Journal of Applied Probability.

[3]  K. Bharath-Kumar,et al.  Discrete-Time Queueing Systems and Their Networks , 1980, IEEE Trans. Commun..

[4]  Moshe Sidi,et al.  Structured priority queueing systems with applications to packet-radio networks , 1983, Perform. Evaluation.

[5]  M. Rumsewicz,et al.  INSENSITIVITY WITH AGE-DEPENDENT ROUTING , 1989 .

[6]  P. Burke,et al.  Behavior of Tandem Buffers with Geometric Input and Markovian Output , 1976, IEEE Trans. Commun..

[7]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[8]  Arie Hordijk,et al.  Networks of queues , 1984 .

[9]  K. Mani Chandy,et al.  A Characterization of Product-Form Queuing Networks , 1983, JACM.

[10]  Hans Daduna,et al.  Networks of queues in discrete time , 1983, Z. Oper. Research.

[11]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[12]  C. E. M. Pearce,et al.  Closed queueing networks with batch services , 1990, Queueing Syst. Theory Appl..

[13]  P. Whittle.  Equilibrium distributions for an open migration process , 1968, Journal of Applied Probability.

[14]  Jean Walrand.  A DISCRETE-TIME QUEUEING NETWORK , 1983 .

[15]  Donald F. Towsley,et al.  On discrete-time queueing systems , 1979 .