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Flow lines with unlimited buffers: M/M/1-systems

Consider a flow-line system with M stations and unlimited buffer capacities. Each station has a single server. The processing times of the jobs are independent and identically distributed exponential random variables with mean b(m), m=1,2,...,M. Jobs arrive at station 1 according to a Poisson process with rate lambda.

Under these assumptions the performance criteria (flow time, queue length) can be computed exactly through analysis of each station as a single-stage M/M/1 queueing system.


m index of stations

mean processing time at station m

Q(m) queue length in front of station m
U(m) utilization of station m


flow time at station m (waiting and processing)


- Buzacott/Shanthikumar (1993), Paragraph 5.4

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