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.

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.

scholarly journals Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule

2016 ◽  
Vol 4 (6) ◽  
pp. 547-559
Author(s):  
Jingjing Ye ◽  
Liwei Liu ◽  
Tao Jiang
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Sojourn Time ◽  
Time Distribution ◽  
Busy Period ◽  
Balance Equations ◽  
Sojourn Time Distribution ◽  
The Mean ◽  
System Length ◽  
Number Of Customers

AbstractThis paper studies a single-sever queue with disasters and repairs, in which after each service completion the server may take a vacation with probabilityq(0≤q≤1), or begin to serve the next customer, if any, with probabilityp(= 1− q). The disaster only affects the system when the server is in operation, and once it occurs, all customers present are eliminated from the system. We obtain the stationary probability generating functions (PGFs) of the number of customers in the system by solving the balance equations of the system. Some performance measures such as the mean system length, the probability that the server is in different states, the rate at which disasters occur and the rate of initiations of busy period are determined. We also derive the sojourn time distribution and the mean sojourn time. In addition, some numerical examples are presented to show the effect of the parameters on the mean system length.

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.

Sign in / Sign up

Export Citation Format

Share Document