Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

1983 ◽  
Vol 15 (04) ◽  
pp. 840-856 ◽  
Author(s):  
J. Keilson ◽  
U. Sumita
Keyword(s):  
Time Distribution ◽  
Arrival Rate ◽  
Priority Queue ◽  
Service Time Distribution ◽  
Transform Method ◽  
Laguerre Transform ◽  
Poisson Stream ◽  
Lindley Process ◽  
Theoretical Results ◽  
Time Sequences

A Poisson stream of arrival rate λI and service-time distribution A I(x) has preempt/resume priority over a second stream of rate λII and distribution A II(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

1983 ◽  
Vol 15 (4) ◽  
pp. 840-856 ◽  
Author(s):  
J. Keilson ◽  
U. Sumita
Keyword(s):  
Time Distribution ◽  
Arrival Rate ◽  
Priority Queue ◽  
Service Time Distribution ◽  
Transform Method ◽  
Laguerre Transform ◽  
Poisson Stream ◽  
Lindley Process ◽  
Theoretical Results ◽  
Time Sequences

A Poisson stream of arrival rate λI and service-time distribution AI(x) has preempt/resume priority over a second stream of rate λII and distribution AII(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

Hitting time in an M/G/1 queue

1999 ◽  
Vol 36 (03) ◽  
pp. 934-940 ◽  
Author(s):  
Sheldon M. Ross ◽  
Sridhar Seshadri
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Arrival Rate ◽  
Hitting Time ◽  
Service Time Distribution ◽  
Expected Time ◽  
Efficient Simulation ◽  
Simulation Procedure ◽  
Poisson Arrival ◽  
Stationary Delay

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

Hitting time in an M/G/1 queue

1999 ◽  
Vol 36 (3) ◽  
pp. 934-940 ◽  
Author(s):  
Sheldon M. Ross ◽  
Sridhar Seshadri
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Arrival Rate ◽  
Hitting Time ◽  
Service Time Distribution ◽  
Expected Time ◽  
Efficient Simulation ◽  
Simulation Procedure ◽  
Poisson Arrival ◽  
Stationary Delay

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

On the service time distribution and the waiting time process of a potentially infinite capacity queueing system

1969 ◽  
Vol 6 (3) ◽  
pp. 594-603 ◽  
Author(s):  
Nasser Hadidi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Poisson Stream ◽  
Waiting Time Process ◽  
The Subject ◽  
Effective Service

In [1] the authors dealt with a particular queueing system in which arrivals occurred in a Poisson stream and the probability differential of a service completion was μσn when the queue contained n customers. Much of the theory could not be carried out further analytically for a general σn, which is a purely n-dependent quantity. To carry the analysis further to the extent of finding the “effective” service time and the waiting time distribution when σn is a linear function of n, (which is considered to be rather general and sufficient for practical purposes), constitutes the subject matter of this paper.

Nonparametric estimation of the service time distribution in the M/G/∞ queue

2016 ◽  
Vol 48 (4) ◽  
pp. 1117-1138 ◽  
Author(s):  
Alexander Goldenshluger
Keyword(s):  
Service Time ◽  
Incomplete Data ◽  
Time Distribution ◽  
Arrival Rate ◽  
Fixed Time ◽  
Time Interval ◽  
Service Time Distribution ◽  
Regular Grid ◽  
Fixed Time Interval ◽  
The Subject

AbstractThe subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well.

Dynamic Performance Evaluation of Communication/Computer Systems with Highly Reliable Components

1988 ◽  
Vol 2 (2) ◽  
pp. 185-213 ◽  
Author(s):  
Peter Kubat ◽  
Ushio Sumita ◽  
Yasushi Masuda
Keyword(s):  
Dynamic Performance ◽  
Task Completion ◽  
Processing Capacity ◽  
Transform Method ◽  
Laguerre Transform ◽  
System Components ◽  
Cumulative System ◽  
Computational Procedures ◽  
Theoretical Results ◽  
Replacement Time

System components of communication/computer networks are quite reliable in that their average uptimes are much larger than the average repair/replacement time of a failed unit. By taking this observation into account, a semiMarkov model is developed with a simple regenerative structure, thereby providing strong analytical and computational tractability. Expressions of a variety of dynamic performability measures, such as the cumulative system processing capacity and the task completion time, are explicitly derived. Computational procedures for evaluating such time-dependent performability measures are developed based on these theoretical results combined with the Laguerre transform method. The power and the efficiency of the computational procedures are demonstrated through a numerical example.

On the service time distribution and the waiting time process of a potentially infinite capacity queueing system

1969 ◽  
Vol 6 (03) ◽  
pp. 594-603 ◽  
Author(s):  
Nasser Hadidi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Poisson Stream ◽  
Waiting Time Process ◽  
The Subject ◽  
Effective Service

In [1] the authors dealt with a particular queueing system in which arrivals occurred in a Poisson stream and the probability differential of a service completion was μσn when the queue contained n customers. Much of the theory could not be carried out further analytically for a general σn , which is a purely n-dependent quantity. To carry the analysis further to the extent of finding the “effective” service time and the waiting time distribution when σn is a linear function of n, (which is considered to be rather general and sufficient for practical purposes), constitutes the subject matter of this paper.

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