On M/G/1 queues with exhaustive service and generalized vacations

1995 ◽  
Vol 27 (2) ◽  
pp. 510-531 ◽  
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Recursive Formula ◽  
Decomposition Property ◽  
Stationary Waiting Time

We consider M/G/1 queues with exhaustive service and generalized vacations, where at the end of every busy period the server either follows a mixed vacation policy from a given vacation policy set or stays idle. A simple recursive formula for the moments of the stationary waiting time is provided. This formula results in the decomposition property for our model immediately. It also enables us to derive many existing results for the M/G/1 queues with various vacation policies.

On M/G/1 queues with exhaustive service and generalized vacations

1995 ◽  
Vol 27 (02) ◽  
pp. 510-531 ◽  
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Recursive Formula ◽  
Decomposition Property ◽  
Stationary Waiting Time

We consider M/G/1 queues with exhaustive service and generalized vacations, where at the end of every busy period the server either follows a mixed vacation policy from a given vacation policy set or stays idle. A simple recursive formula for the moments of the stationary waiting time is provided. This formula results in the decomposition property for our model immediately. It also enables us to derive many existing results for the M/G/1 queues with various vacation policies.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (4) ◽  
pp. 1083-1097 ◽  
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

scholarly journals The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1

1962 ◽  
Vol 2 (3) ◽  
pp. 345-356 ◽  
Author(s):  
J. F. C. Kingmán
Keyword(s):  
Random Walk ◽  
Characteristic Function ◽  
Waiting Time ◽  
Time Distribution ◽  
Busy Period ◽  
Waiting Time Distribution ◽  
Period Distribution ◽  
Stationary Waiting Time

As an illustration of the use of his identity [10], Spitzer [11] obtained the Pollaczek-Khintchine formula for the waiting time distribution of the queue M/G/1. The present paper develops this approach, using a generalised form of Spitzer's identity applied to a three-demensional random walk. This yields a number of results for the general queue GI/G/1, including Smith' solution for the stationary waiting time, which is established under less restrictive conditions that hitherto (§ 5). A soultion is obtained for the busy period distribution in GI/G/1 (§ 7) which can be evaluated when either of the distributions concerned has a rational characteristic function. This solution contains some recent results of Conolly on the quene GI/En/1, as well as well-known results for M/G/1.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (04) ◽  
pp. 1083-1097
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

scholarly journals Preemptive priority queues

1963 ◽  
Vol 3 (4) ◽  
pp. 491-502 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Priority Queues ◽  
Poisson Processes ◽  
Size Distributions ◽  
Queue Size ◽  
Preemptive Priority ◽  
Preemptive Resume ◽  
Stationary Waiting Time

SummaryIn this paper priority queues with K classes of customers with a preemptive repeat and a preemptive resume policy are considered. Customers arrive in independent Poisson processes, are served, within classes, in order of arrival, and have general requirements for service. Transforms of stationary waiting time and queue size distributions and busy period distributions are obtained for individual classes and for the system; the moments of the distributions are considered.

scholarly journals Decomposition of M/M/1 With Unreliable Service and a Working Vacation

2020 ◽  
Vol 9 (1) ◽  
pp. 63
Author(s):  
Joshua Patterson ◽  
Andrzej Korzeniowski
Keyword(s):  
Closed Form ◽  
Failure Rate ◽  
Waiting Time ◽  
Queue Length ◽  
Service Failure ◽  
Working Vacation ◽  
Stationary Queue Length ◽  
Stationary Waiting Time ◽  
Relationship Of ◽  
The Relationship

We use the stationary distribution for the M/M/1 with Unreliable Service and aWorking Vacation (M/M/1/US/WV) given explicitly in (Patterson & Korzeniowski, 2019) to find a decomposition of the stationary queue length N. By applying the distributional form of Little's Law the Laplace-tieltjes Transform of the stationary customer waiting time W is derived. The closed form of the expected value and variance for both N and W is found and the relationship of the expected stationary waiting time as a function of the service failure rate is determined.

scholarly journals Single server queues with modified service mechanisms

1962 ◽  
Vol 2 (4) ◽  
pp. 499-507 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Time Distribution ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Period Distribution ◽  
Time Dependent Problem ◽  
Stationary Waiting Time ◽  
Special Case

SummaryThis paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.

Another martingale bound on the waiting-time distribution in GI/G/1 queues

1979 ◽  
Vol 16 (2) ◽  
pp. 454-457 ◽  
Author(s):  
Harry H. Tan
Keyword(s):  
Waiting Time ◽  
Upper Bound ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Martingale Approach ◽  
Stationary Waiting Time

A new upper bound on the stationary waiting-time distribution of a GI/G/1 queue is derived following Kingman's martingale approach. This bound is generally stronger than Kingman's upper bound and is sometimes stronger than an upper bound derived by Ross.

Sign in / Sign up

Export Citation Format

Share Document