Queueing analysis of a jockeying model
In this paper, we
solve a type of shortest queue problem, which is related to
multibeam satellite systems. We assume that the
packet interarrival times are independently distributed
according to an arbitrary distribution function,
that the service times are Markovian with possibly different
service rates, that each of the servers has
its own buffer for packet waiting, and that jockeying among
buffers is permitted. Packets always join the shortest
buffer(s).
Jockeying takes place as soon as
the difference between the longest and shortest buffers exceeds
a pre-set number (not necessary 1).
In this case, the last packet in a longest buffer jockeys instantaneously
to the shortest buffer(s).
We prove that the equilibrium distribution of
packets in the system is modified vector-geometric. Expressions of main performance
measures, including the average number of packets in
the system, the average packet waiting time in the system
and the average number of jockeying,
are given. Based on the above solutions, numerical results
are computed. By comparing the results for jockeying and non-jockeying
models, we show that a significant improvement of the system
performance is achieved for the jockeying model.
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