Simple Approximations for Second Moment Characteristics of the Sojourn Time in the M/G/1 Processor Sharing Queue

1989 ◽  
pp. 105-120 ◽  
Author(s):  
J. L. van den Berg
Keyword(s):  
Sojourn Time ◽  
Processor Sharing ◽  
Second Moment

scholarly journals Processor-sharing and random-service queues with semi-Markovian arrivals

2005 ◽  
Vol 42 (02) ◽  
pp. 478-490
Author(s):  
De-An Wu ◽  
Hideaki Takagi
Keyword(s):  
Waiting Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Interarrival Time ◽  
Size Distributions ◽  
Processor Sharing ◽  
Queue Size ◽  
Mean Waiting Time ◽  
The Mean

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-lcustomer who, upon his arrival, meetskcustomers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-lcustomer who, upon his arrival, meetsk+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.

Sojourn-time approximations for a multi-server processor sharing system with priorities

2003 ◽  
Vol 54 (3) ◽  
pp. 249-261 ◽  
Author(s):  
R.D. van der Mei ◽  
J.L. van den Berg ◽  
R. Vranken ◽  
B.M.M. Gijsen
Keyword(s):  
Sojourn Time ◽  
Processor Sharing ◽  
Multi Server

The sojourn time in the GI/M/1 queue by processor sharing

1984 ◽  
Vol 21 (2) ◽  
pp. 437-442 ◽  
Author(s):  
V. Ramaswami
Keyword(s):  
Sojourn Time ◽  
Queueing Model ◽  
Processor Sharing ◽  
Computer Engineering ◽  
The Mean

A queueing model of considerable interest in computer engineering is the processor-sharing model in which the server shares its fixed capacity equally among all units present in the system. Here, we derive the mean and the variance of the equilibrium sojourn time, and deduce that the variance of the sojourn time is larger for the processor-sharing model than for the corresponding FCFS model.

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