The conditional sojourn time distribution in the GI/M/1 processor-sharing queue in heavy traffic

1993 ◽  
Vol 14 (1-2) ◽  
pp. 99-109 ◽  
Author(s):  
Xiaoming Tan ◽  
Yongzhi Yang ◽  
Charles Knessl
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Sojourn Time Distribution

The sojourn-time distribution in the M/G/1 queue by processor sharing

1984 ◽  
Vol 21 (02) ◽  
pp. 360-378
Author(s):  
Teunis J. Ott
Keyword(s):  
Generating Functions ◽  
Sojourn Time ◽  
Time Distribution ◽  
Joint Distribution ◽  
Processor Sharing ◽  
Explicit Formulas ◽  
Sojourn Time Distribution ◽  
Number Of Customers ◽  
Stieltjes Transforms

This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers in the general M/G/1 queue with processor sharing (M/G/1/PS). Explicit formulas are given for a number of conditional and unconditional moments, including the variance of the sojourn time of an ‘arbitrary' customer.

Sojourn time distribution in some processor-shared queues

1993 ◽  
Vol 4 (4) ◽  
pp. 437-448
Author(s):  
Xiaoming Tan ◽  
Charles Knessl
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Perturbation Methods ◽  
Asymptotic Properties ◽  
Processor Sharing ◽  
Finite Capacity ◽  
Capacity Model ◽  
Sojourn Time Distribution ◽  
Processor Sharing Queues ◽  
Finite Capacity Queue

We develop a technique for obtaining asymptotic properties of the sojourn time distribution in processor-sharing queues. We treat the standard M/M/1-PS queue and its finite capacity version, the M/M/1/K-PS queue. Using perturbation methods, we construct asymptotic expansions for the distribution of a tagged customer's sojourn time, conditioned on that customer's total required service. The asymptotic limit assumes that (i) the traffic intensity is close to one for the infinite capacity model, and (ii) that the system's capacity is large for the finite capacity queue.

The sojourn-time distribution in the M/G/1 queue by processor sharing

1984 ◽  
Vol 21 (2) ◽  
pp. 360-378 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Generating Functions ◽  
Sojourn Time ◽  
Time Distribution ◽  
Joint Distribution ◽  
Processor Sharing ◽  
Explicit Formulas ◽  
Sojourn Time Distribution ◽  
Number Of Customers ◽  
Stieltjes Transforms

This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers in the general M/G/1 queue with processor sharing (M/G/1/PS).Explicit formulas are given for a number of conditional and unconditional moments, including the variance of the sojourn time of an ‘arbitrary' customer.

Sign in / Sign up

Export Citation Format

Share Document