Local balance in queueing networks with positive and negative customers
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This paper investigates to what extent a recently developed new product form result for queueing networks with positive and negative customers fits into the class of product form queueing networks that satisfy a notion of partial or local balance. As such, this paper investigates whether this new product form is still a consequence of an appropriate notion of local balance. To this end, a new and non-standard type of local balance is introduced as an extension of standard local balance. This new type of local balance appears more restrictive and is no longer directly sufficient for global balance. Nevertheless, based on this new type of local balance, some extensions such as blocking phenomena for queueing networks with positive and negative customers can be concluded.
- Baskett, F., Chandy, K.M., Muntz, R.R., Palacios, F.G. (1975) Open, closed and mixed networks of queues with different classes of customers. J.ACM 22: pp. 248-260
- Boucherie, R.J., Dijk, N.M. (1990) Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes. Adv. Appl. Prob. 22: pp. 433-455
- Boucherie, R.J., Dijk, N.M. (1991) Product forms for queueing networks with state dependent multiple job transitions. Adv. Appl. Prob. 23: pp. 152-187
- Gelenbe, E. (1989) Random neural networks with negative and positive signals and product form solution. Neural Comp. 1: pp. 502-510
- Gelenbe, E. (1991) Product form queueing networks with negative and positive customers. J. Appl. Prob. 28: pp. 656-663
- W. Henderson, B.S. Northcote and P.G. Taylor, Geometric equilibrium distributions for queues with interactive batch departures, Ann. Oper. Res. 48 (1993), this volume.
- Henderson, W., Pearce, C.E.M., Taylor, P.G., Dijk, N.M. (1990) Closed queueing networks with batch services. Queueing Syst. 6: pp. 59-70
- Hordijk, A., Dijk, N.M. (1983) Networks of Queues, Part I: Job-local-balance and the adjoint process; Part II: General routing and service characteristics. Lecture Notes in Control and Informational Sciences 60: pp. 158-205
- Jackson, J.R. (1963) Jobshop-like queueing systems. Manag. Sci. 10: pp. 131-142
- F.P. Kelly,Reversibility and Stochastic Networks (Wiley, 1975).
- Serfozo, R.F. (1989) Markovian network processes: congestion dependent routing and processing. Queueing Syst. 5: pp. 5-36
- P. Whittle,Systems in Stochastic Equilibrium (Wiley, 1986).
- Local balance in queueing networks with positive and negative customers
Annals of Operations Research
Volume 48, Issue 5 , pp 463-492
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- Print ISSN
- Online ISSN
- Baltzer Science Publishers, Baarn/Kluwer Academic Publishers
- Additional Links
- Local balance
- negative customers
- product form
- queueing network
- traffic equations
- Industry Sectors