Interconnected networks of queues with randomized arrival and departure blocking

In this paper, we study two interconnected multiclass non-exponential queueing networks. Jobs can jump from one cluster to another, but subject to randomized blocking depending on the class occupancies. Such systems naturally arise in communication networks, like Metropolitan Area Networks. We present sufficient conditions for the existence of a product form equilibrium distribution under both the recirculate and the stop blocking protocol. A number of examples are given.

[1]  Ian F. Akyildiz,et al.  Exact Solution for Networks of Parallel Queues with Finite Buffers , 1990, Performance.

[2]  R. Schassberger.  Insensitivity of Steady-state Distributions of Generalized Semi-Markov Processes. Part II , 1977 .

[3]  P. Whittle.  Partial balance and insensitivity , 1985, Journal of Applied Probability.

[4]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[5]  Simon S. Lam,et al.  Queuing Networks with Population Size Constraints , 1977, IBM J. Res. Dev..

[6]  J. R. Jackson.  Networks of Waiting Lines , 1957 .

[7]  N M van Dijk,et al.  Insensitivity in two-node blocking models with applications , 1986 .

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

[9]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[10]  J. Lehoczky,et al.  Insensitivity of blocking probabilities in a circuit-switching network , 1984 .

[11]  Donald F. Towsley,et al.  Queuing Network Models with State-Dependent Routing , 1980, JACM.

[12]  G. J. Foschini,et al.  Sharing Memory Optimally , 1983, IEEE Trans. Commun..

[13]  Adrian E. Conway,et al.  Product-Form and Insensitivity in Circuit-Switched Networks with Failing Links , 1989, Perform. Evaluation.

[14]  Anthony E. Krzesinski.  Multiclass Queueing Networks with State-Dependent Routing , 1987, Perform. Evaluation.

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

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

[17]  W. J. Gordon,et al.  Closed Queuing Systems with Exponential Servers , 1967, Oper. Res..

[18]  Boris G. Pittel,et al.  Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis , 1979, Math. Oper. Res..

[19]  R. Schassberger.  Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds , 1978, Advances in Applied Probability.

[20]  Arie Hordijk,et al.  Stationary Probabilities for Networks of Queues , 1982 .

[21]  Peter Whittle,et al.  Systems in stochastic equilibrium , 1986 .

[22]  J. Kaufman,et al.  Blocking in a Shared Resource Environment , 1981, IEEE Trans. Commun..

[23]  Harry G. Perros,et al.  On equivalencies of blocking mechanisms in queueing networks with blocking , 1986 .

[24]  Izhak Rubin,et al.  Performance analysis of interconnected metropolitan area circuit-switched telecommunications networks , 1988, IEEE Trans. Commun..

[25]  N. M. van Dijk,et al.  Product forms for queueing networks with limited clusters , 1988 .

[26]  David D. Yao,et al.  Modeling a Class of Flexible Manufacturing Systems with Reversible Routing , 1987, Oper. Res..

[27]  P. Moran,et al.  Reversibility and Stochastic Networks , 1980 .