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Introduction
Published in Joseph Y.-T. Leung, Handbook of SCHEDULING, 2004
[16] X. Chao and M. Pinedo, (1995), Queueing networks with signals and stage dependent routing. Probability in the Engineering and Informational Sciences, 9, 341–354. [17] X. Chao and M. Pinedo, (1995), On networks of queues with batch services, signals, and product form solution. Operations Research Letters, 237–242.
Queueing Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
The system is said to have a product-form solution because the joint steady-state probabilities can be shown to equal the product of the steady-state probabilities for the individual queues. The product-form solution implies that the queues in series can be treated as independent M/M/1 queues.
Queuing Analysis and Optimization Techniques
Published in We-Min Chow, Assembly Line Design, 2020
Equation (3.28) characterizes an important property of a class of queuing networks, namely, the product form solution. Computational effort is greatly simplified. Since the queue lengths of individual centers are independent of each other, one may evaluate one service center at a time.
G-network models to support planning for disaster relief distribution
Published in International Journal of Production Research, 2022
Merve Ozen, Ananth Krishnamurthy
The articles (Artalejo 2000; Bocharov and Vishnevskii 2003) provide detailed surveys on G-network models and discussion on applications of G-networks including inventory systems, manufacturing and inspection operations. Gelenbe, Glynn, and Sigman (1991); Gelenbe (1991) introduced the first product form results for G-networks, followed by Gelenbe (1993) analysing G-networks with signals. The G-network theory has later been extended to cover multi-class arrivals (Gelenbe and Labed 1998), generally distributed service times (Harrison and Pitel 1996), state dependent service times (Bocharov et al. 2004a, 2004b) and tandem queues with blocking (Gomez-Corral 2002). In this paper, the G-network model of relief centers allows single or batch transfer of victims between queues in the network triggered by a signal arrival. The literature has shown existence of product form results for networks where signals only cause batch removal of customers from the network (Gelenbe 1993), networks with batch service (Chao and Pinedo 1995) and networks with batch arrival and batch service (Miyazawa and Taylor 1997). To our knowledge there is no prior work investigating existence of product form solution for a generalised queuing network with signals causing batch transfers of customers between queues in the network. This paper attempts to fill this gap.