Open finite queueing networks with M/M/C/K parallel servers☆
References (68)
Approximate analysis of exponential tandem queues with blocking
Europ. J. Ops Res.
(1982)- et al.
Asymptotic behaviour of the expansion method for open finite queueing networks
Computers Ops Res.
(1988) - et al.
Some equivalencies on closed queueing networks with blocking
Perform. Eval.
(1989) Exact product form solutions for queueing networks with blocking
IEEE Trans. Computers
(1987)On the exact and approximate throughput analysis of closed queueing networks with blocking
IEEE Trans. Softw. Engng
(1988)Exact analysis of queueing networks with rejection blocking
Probability, Statistics, and Queueing Theory with Computer Applications
(1978)- et al.
Open networks of queues with blocking: split and merge configurations
IIE Trans.
(1986) - et al.
Open, closed, and mixed networks of queues with different classes of customers
J. ACM
(1975) - et al.
Approximate analysis of exponential queuing systems with blocking
Acta Inform.
(1981)
An approximation method for tandem queues with blocking
Ops Res.
Approximate queueing models of dynamic job shops
Mgmt Sci.
Throughput capacity of a sequence of queues with blocking due to finite waiting room
IEEE Trans. Soft. Engng
Approximate methods for analyzing queueing network models of computing systems
Computer Surv.
Sensitivity analysis in open finite queueing networks
State dependent queueing models
A decomposition method for the approximate analysis of closed queueing networks with blocking
Optimal routing and buffer space allocation in series-parallel queueing networks
Real time routing in finite queueing networks
Queueing networks: a survey of their random processes
SIAM Rev.
Approximations to stochastic service systems with an application to a retrial model
Bell Sys. Tech. J.
Congestion in blocking systems — a simple approximation technique
Bell Sys. Tech. J.
The behavior of a single queue in a general queueing network
ACTA INF
Closed queueing systems with exponential servers
Ops Res.
Cyclic queueing systems with restricted length queues
Ops Res.
Heavy traffice multi-commodity routing in open finite queueing networks
Queueing network models of computer systems
ACM Comput. Surv.
Fundamentals of Queueing Theory
Annotated bibliography of blocking systems
An approximation method for general tandem queueing systems subject to blocking
A diffusion approximation solution to the G/G/k queueing system
Computers Ops Res.
Approximate analysis of M/M/C/K queueing networks
Cited by (39)
Application of system dynamics for analysis of performance of manufacturing systems
2019, Journal of Manufacturing SystemsApproximation of throughput in tandem queues with multiple servers and blocking
2014, Applied Mathematical ModellingCitation Excerpt :The literature on the analysis of tandem queues with multiple servers and finite buffer is more scarce than the single server system. Maximum entropy method [20] and expansion method [21] are presented for approximation of the subsystem in multi-server queueing networks with finite buffers and exponential distribution of service time. van Vuuren et al. [22] decomposed the tandem queue with parallel reliable servers and general distribution of service time into subsystems with two service stations and one buffer space, and then approximate each multi-server subsystem by an aggregated single (super) server queue with state-dependent inter-arrival and service times.
Near optimal buffer allocation in remanufacturing systems with N-policy
2010, Computers and Industrial EngineeringCitation Excerpt :After decomposing the network, we use the expansion methodology to analyze each node individually. The expansion methodology is an efficient tool for the analysis of nodes with finite buffers (Jain & Smith, 1994; Kerbache & Smith, 1987; Kerbache & Smith, 1988; Singh & Smith, 1997; Smith & Daskalaki, 1988). In this methodology, we expand the network by adding an extra node in front of each finite buffer node.
Performance optimization of open zero-buffer multi-server queueing networks
2010, Computers and Operations ResearchCitation Excerpt :We compare our results with simulation, and show that the generalized expansion method (GEM) proposed by Kerbache and Smith [9] gives an excellent approximation for the performance measures of the zero-buffer systems studied. We show that the GEM delivers results with an accuracy mostly less than 5% (with maxima up to 16% for heavy congested systems, similar as in [8]), for basic series, merge, and split topologies, both symmetrical and asymmetrical. We present a multi-objective optimization methodology for zero-buffer systems, which provides particularly insightful results.
Optimal buffer allocation in finite closed networks with multiple servers
2008, Computers and Operations ResearchBuffer allocation plan for a remanufacturing cell
2005, Computers and Industrial Engineering
- ☆
Research supported by Grants from the National Science Foundation #MSM-8715152, MSS-9116666.
- ‡
S. Jain is a consultant with American Airlines Decision Technologies. He is interested in mathematical programming applications especially in the areas of transportation and logistics. He graduated from the University of Massachusetts with an M.Sci. degree in Industrial Engineering and Operations Research. His thesis was the basis for the article published here.
- §
J. MacGregor Smith received his Bachelors and Masters of Architecture from the University of California at Berkeley and his Ph.D. in Mechanical and Industrial Engineering from the University of Illinois at Chapaign-Urbana. He is also a registered architect. His academic and professional interests include the design of algorithms for combinatorial optimization and stochastic network problems, the optimal design of facilities, networks, and the design and analysis of manufacturing systems.