The Fluid Limit of the Critical Processor Sharing Tandem Queue

A sequence of finite tandem queue is considered for
this study. Each one has a single server, which operates under the
egalitarian processor sharing discipline. External customers arrive at
each queue according to a renewal input process and having a general
service times distribution. Upon completing service, customers leave
the current queue and enter to the next. Under mild assumptions,
including critical data, we prove the existence and the uniqueness
of the fluid solution. For asymptotic behavior, we provide necessary
and sufficient conditions for the invariant state and the convergence
to this invariant state. In the end, we establish the convergence of a
correctly normalized state process to a fluid limit characterized by a
system of algebraic and integral equations.

Authors:

• Amal Ezzidani
• Abdelghani Ben Tahar
• Mohamed Hanini

Keywords:

• Fluid Limit
• fluid model
• measure valued process
• processor sharing
• tandem queue.

References:

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