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Summary: Queueing Systems 20 (1995) 395-407 395
Optimal buffer allocation in tandems of last come
first served queues
V. Anantharam a'1 and A. Ganeshb'2
aDepartmentof ElectricalEngineeringand ComputerScience,
Universityof California,Berkeley, CA 94720, USA
bDepartmentof ComputerScience, Universityof Edinburgh,
EdinburghEH9 3JZ, UK
Received 23 September 1994; revised 21 March 1995
A large fixed number of buffer spaces is given. We consider the problem of
allocating these spaces among the nodes of a tandem of last-come-first-servedqueues
with general service time distributions and Poisson external arrivals so as to optimize
some performance criterion associated with the time to buffer overflow, such as
maximizing its mean or maximizing the probability that it exceeds some value.
Consider the following rule of thumb: allocate the buffer spaces in inverse proportion
to the logarithms of the effective service rates at the nodes. Here effective service rate
denotes the ratio of the service rate to the stationary arrival rate. We prove that this
rule of thumb achieves a nearly optimal buffer allocation under the assumption that
the service time distributions satisfy an exponential tail condition. This problem has
been studied earlier in the context of Jackson networks, where it was shown that the
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