On the sojourn times for many-queue head-of-the-line Processor-sharing systems with permanent customers

1998 ◽  
Vol 47 (2) ◽  
pp. 181-220 ◽  
Author(s):  
Andreas Brandt ◽  
Manfred Brandt
Keyword(s):  
Processor Sharing ◽  
Sojourn Times ◽  
Permanent Customers

The M/G/1 processor sharing queue as the almost sure limit of feedback queues

1990 ◽  
Vol 27 (4) ◽  
pp. 913-918 ◽  
Author(s):  
J. A. C. Resing ◽  
G. Hooghiemstra ◽  
M. S. Keane
Keyword(s):  
Almost Sure Convergence ◽  
Processor Sharing ◽  
Regenerative Processes ◽  
Arrival Times ◽  
Sojourn Times ◽  
Feedback Model ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Feedback Queue ◽  
Feedback Queues

In the paper a probabilistic coupling between the M/G/1 processor sharing queue and the M/M/1 feedback queue, with general feedback probabilities, is established. This coupling is then used to prove the almost sure convergence of sojourn times in the feedback model to sojourn times in the M/G/1 processor sharing queue. Using the theory of regenerative processes it follows that for stable queues the stationary distribution of the sojourn time in the feedback model converges in law to the corresponding distribution in the processor sharing model. The results do not depend on Poisson arrival times, but are also valid for general arrival processes.

The M/G/1 processor sharing queue as the almost sure limit of feedback queues

1990 ◽  
Vol 27 (04) ◽  
pp. 913-918 ◽  
Author(s):  
J. A. C. Resing ◽  
G. Hooghiemstra ◽  
M. S. Keane
Keyword(s):  
Almost Sure Convergence ◽  
Processor Sharing ◽  
Regenerative Processes ◽  
Arrival Times ◽  
Sojourn Times ◽  
Feedback Model ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Feedback Queue ◽  
Feedback Queues

In the paper a probabilistic coupling between the M/G/1 processor sharing queue and the M/M/1 feedback queue, with general feedback probabilities, is established. This coupling is then used to prove the almost sure convergence of sojourn times in the feedback model to sojourn times in the M/G/1 processor sharing queue. Using the theory of regenerative processes it follows that for stable queues the stationary distribution of the sojourn time in the feedback model converges in law to the corresponding distribution in the processor sharing model. The results do not depend on Poisson arrival times, but are also valid for general arrival processes.

On sojourn times in M/GI systems under state-dependent processor sharing

2009 ◽  
Vol 64 (2) ◽  
pp. 167-201 ◽  
Author(s):  
Manfred Brandt ◽  
Andreas Brandt
Keyword(s):  
Processor Sharing ◽  
Sojourn Times ◽  
State Dependent

scholarly journals Sojourn times in a processor sharing queue with multiple vacations

2012 ◽  
Vol 71 (1-2) ◽  
pp. 53-78 ◽  
Author(s):  
U. Ayesta ◽  
O. J. Boxma ◽  
I. M. Verloop
Keyword(s):  
Processor Sharing ◽  
Multiple Vacations ◽  
Sojourn Times
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