Characterizations of the Exponential Distribution via the Blocking Time in a Queueing System with an Unreliable Server

1998 ◽  
Vol 35 (1) ◽  
pp. 236-239 ◽  
Author(s):  
Jian-Lun Xu
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Coefficient Of Variation ◽  
Queueing System ◽  
Random Variables ◽  
Unreliable Server ◽  
Failure Times ◽  
Server Failure

The characterization of the exponential distribution via the coefficient of the variation of the blocking time in a queueing system with an unreliable server, as given by Lin (1993), is improved by substantially weakening the conditions. Based on the coefficient of variation of certain random variables, including the blocking time, the normal service time and the minimum of the normal service and the server failure times, two new characterizations of the exponential distribution are obtained.

Characterizations of the Exponential Distribution via the Blocking Time in a Queueing System with an Unreliable Server

1998 ◽  
Vol 35 (01) ◽  
pp. 236-239
Author(s):  
Jian-Lun Xu
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Coefficient Of Variation ◽  
Queueing System ◽  
Random Variables ◽  
Unreliable Server ◽  
Failure Times ◽  
Server Failure

The characterization of the exponential distribution via the coefficient of the variation of the blocking time in a queueing system with an unreliable server, as given by Lin (1993), is improved by substantially weakening the conditions. Based on the coefficient of variation of certain random variables, including the blocking time, the normal service time and the minimum of the normal service and the server failure times, two new characterizations of the exponential distribution are obtained.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

The Service Time Properties of an Unreliable Server Characterize the Exponential Distribution

1994 ◽  
Vol 26 (01) ◽  
pp. 172-182 ◽  
Author(s):  
Z. Khalil ◽  
B. Dimitrov
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Initial Conditions ◽  
Mean Values ◽  
Unreliable Server ◽  
Service Disciplines ◽  
The Mean ◽  
Server Reliability ◽  
Preemptive Repeat Different

Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

scholarly journals MX/G/1 Vacation Queueing System with Two Types of Repair facilities and Server Timeout

2019 ◽  
Vol 8 (9) ◽  
pp. 2040-2043
Keyword(s):  
Size Distribution ◽  
Exponential Distribution ◽  
Service Time ◽  
Queueing System ◽  
Batch Size ◽  
Single Server ◽  
Poisson Arrivals ◽  
Server Failure ◽  
System Length ◽  
General Service

We consider a single server vacation queue with two types of repair facilities and server timeout. Here customers are in compound Poisson arrivals with general service time and the lifetime of the server follows an exponential distribution. The server find if the system is empty, then he will wait until the time ‘c’. At this time if no one customer arrives into the system, then the server takes vacation otherwise the server commence the service to the arrived customers exhaustively. If the system had broken down immediately, it is sent for repair. Here server failure can be rectified in two case types of repair facilities, case1, as failure happens during customer being served willstays in service facility with a probability of 1-q to complete the remaining service and in case2 it opts for new service also who joins in the head of the queue with probability q. Obtained an expression for the expected system length for different batch size distribution and also numerical results are shown

An unreliable server characterization of the exponential distribution

1994 ◽  
Vol 31 (1) ◽  
pp. 274-279 ◽  
Author(s):  
Janos Galambos ◽  
Charles Hagwood
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Service Time ◽  
Unreliable Server ◽  
Memory Property ◽  
Lack Of Memory Property

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.

An unreliable server characterization of the exponential distribution

1994 ◽  
Vol 31 (01) ◽  
pp. 274-279 ◽  
Author(s):  
Janos Galambos ◽  
Charles Hagwood
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Service Time ◽  
Unreliable Server ◽  
Memory Property ◽  
Lack Of Memory Property

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.

On a new characterization of the exponential distribution related to a queueing system with an unreliable server

1990 ◽  
Vol 27 (1) ◽  
pp. 221-226 ◽  
Author(s):  
B. Dimitrov ◽  
Z. Khalil
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Single Server ◽  
Unreliable Server ◽  
Exponential Law

In this paper we derive a new property of the exponential distribution, closely related to a single-server queueing system with unreliable server. We show that this new property is another characterization of the exponential law.

The Service Time Properties of an Unreliable Server Characterize the Exponential Distribution

1994 ◽  
Vol 26 (1) ◽  
pp. 172-182 ◽  
Author(s):  
Z. Khalil ◽  
B. Dimitrov
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Initial Conditions ◽  
Mean Values ◽  
Unreliable Server ◽  
Service Disciplines ◽  
The Mean ◽  
Server Reliability ◽  
Preemptive Repeat Different

Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

On a new characterization of the exponential distribution related to a queueing system with an unreliable server

1990 ◽  
Vol 27 (01) ◽  
pp. 221-226 ◽  
Author(s):  
B. Dimitrov ◽  
Z. Khalil
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Single Server ◽  
Unreliable Server ◽  
Exponential Law

In this paper we derive a new property of the exponential distribution, closely related to a single-server queueing system with unreliable server. We show that this new property is another characterization of the exponential law.

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