Combining Routing and Buffer Allocation Problems in Series-Parallel Queueing Networks

Systems often have two or more stages and a customer must go several stages before finalizing their service. The systems can be arranged in series or in network. Chapter 5 is dedicated specifically to the performance analysis of systems that have several stages both in series and those that have network arrangement; the theorems of Burke and Jackson are presented; the calculations of the flow and variability in a network and of the measures of performance (cycle time and work in process) are also exposed. Several codes are proposed in Scilab Language to perform calculations automatically. The chapter ends with a section devoted to identifying and analyzing the bottleneck in a system from a cost approach.

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Structured buffer-allocation problems

Discrete Event Dynamic Systems ◽

10.1007/bf01796782 ◽

1996 ◽

Vol 6 (1) ◽

pp. 9-41 ◽

Cited By ~ 21

Author(s):

Paul Glasserman ◽

David D. Yao

Keyword(s):

Buffer Allocation ◽

Allocation Problems

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Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems

Computers & Operations Research ◽

10.1016/j.cor.2012.02.002 ◽

2012 ◽

Vol 39 (11) ◽

pp. 2688-2704 ◽

Cited By ~ 51

Author(s):

Tsung-Jung Hsieh ◽

Wei-Chang Yeh

Keyword(s):

Parallel Systems ◽

Redundancy Allocation ◽

Allocation Problems ◽

In Series

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The buffer allocation problem for general finite buffer queueing networks

IIE Transactions ◽

10.1080/07408170590916986 ◽

2005 ◽

Vol 37 (4) ◽

pp. 343-365 ◽

Cited By ~ 55

Author(s):

J. MACGREGOR SMITH ◽

F. R. B. CRUZ

Keyword(s):

Queueing Networks ◽

Allocation Problem ◽

Finite Buffer ◽

Buffer Allocation

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Rare events in series of queues

Journal of Applied Probability ◽

10.2307/3214800 ◽

1992 ◽

Vol 29 (1) ◽

pp. 168-175 ◽

Cited By ~ 24

Author(s):

Pantelis Tsoucas

Keyword(s):

Queueing Networks ◽

Total Population ◽

Large Deviation ◽

Rare Event ◽

Arrival Rate ◽

Service Rate ◽

Action Functional ◽

In Series ◽

Service Rates ◽

Queues In Series

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

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