Eric Järpe and David Svensson
Department of mathematical statistics, Chalmers University of Technology and Göteborg University. (Masters thesis)
Abstract
Is anything gained, according to queue length, waiting times or busy periods in a FIFO queueing system, by trading human service (stochastic service times) for machinery service (deterministic service times)?
We compare two queueing systems (M/M/k and M/D/k) and show as a limit result that the expected queue length of M/M/k is twice the expected queue length of M/D/k during heavy traffic (i.e. when arrival intensity,
, is equal to service intensity,
,
times number of service stations, k ).
Moreover, we simulate these systems, with time independent
arrival intensity (which confirmes the previous analytical
results), as well as with time dependent (which indicates
similar relationships). Finally, in the case with one
deterministic service station, the queue length is shown
to be stochastically increasing in the arrival intensity
and stochastically decreasing in the service intensity.
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