1
Copyright 2002, Sanjay K. Bose 1
Priority Operation
of
The M/G/1 Queue
Copyright 2002, Sanjay K. Bose 2
P1 2
Class
Class 1 Lowest Priority Class
Head of Line (HOL) Priority Operation of M/G/1 Queue
2
Copyright 2002, Sanjay K. Bose 3
Priority Discipline
Non-Preemptive Preemptive
Preemptive
Resume
Preemptive
Non-Resume
work conserving
disciplines
Copyright 2002, Sanjay K. Bose 4
Non-Preemptive Priority
•Consider an arrival of priority class j when the server is serving
a job of lower priority class k, j>k.
•The new arrival, in spite of being of a priority level higher than
the current job in service, will not interrupt the on-going service.
•Instead, it will join the queue (FCFS) at the end of the queue of
its own priority class, i.e. Class j, and wait for the current job to
finish service.
•Normal HOL priority operation will resume once the on-going
service is over
On-going service is not interrupted, even if there are new
arrivals of higher priority
Work-conserving Discipline
3
Copyright 2002, Sanjay K. Bose 5
Preemptive Resume Priority
•Consider an arrival of priority class j when the server is serving a
job of lower priority class k, j>k.
•The new arrival of class j will immediately preempt the lower
priority job currently being served and will start its own service.
•When service to the previously preempted class k job eventually
resumes (possibly after service to the preempting job of class j and
other jobs of priority higher than k), the service is resumed from
the point where it was interrupted earlier.
On-going service interrupted by arrival of higher priority.
Work already done for the preempted job is remembered
Work-conserving Discipline
Copyright 2002, Sanjay K. Bose 6
Preemptive Non-Resume Priority
•Consider an arrival of priority class j when the server is serving a
job of lower priority class k, j>k.
•The new arrival of class j will immediately preempt the lower
priority job currently being served and will start its own service.
•When service to the previously preempted class k job eventually
resumes (possibly after service to the preempting job of class j and
other jobs of priority higher than k), the service will start afresh
without remembering the service that has already been provided.
On-going service interrupted by arrival of higher priority.
Work already done for the preempted job is not remembered
Work is not conserved
4
Copyright 2002, Sanjay K. Bose 7
• Arrival Process for Class i is Poisson with rate λ
i
i=1,….,P
• Arrival Processes of different classes independent of each
other
• The overall arrival process will also be Poisson with rate λ
∑
=
=
P
i
i
1
λλ
Copyright 2002, Sanjay K. Bose 8
Service time for Class i has mean and second moment
with pdf b
i
(t), cdf B
i
(t) and L.T. of the pdf as L
bi
(s)
i
X
2
i
X
Service times for the different classes assumed to be independent
of each other
Traffic of priority class i
iii
Xλρ =
Total Traffic
X
P
i
i
λρρ ==
∑
=1
where
i
P
i
i
XX
∑
=
=
1
λ
λ
is the mean overall service time
i=1,…..,P
