Approximate Formula of Delay-Time Variance in Renewal-Input General-Service-Time Single-Server Queueing System

2012 ◽  
pp. 503-508
Author(s):  
Yoshitaka Takahashi ◽  
Yoshiaki Shikata ◽  
Andreas Frey
Keyword(s):  
Service Time ◽  
Delay Time ◽  
Approximate Formula ◽  
Queueing System ◽  
Single Server ◽  
Time Variance ◽  
General Service

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

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (3) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

A queueing system with impatient customers

1985 ◽  
Vol 22 (3) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (03) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution. All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

On the ordering of tandem queues with exponential servers

1986 ◽  
Vol 23 (01) ◽  
pp. 115-129 ◽  
Author(s):  
Tapani Lehtonen
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Tandem Queues ◽  
Departure Process ◽  
Service Stations ◽  
Service Rates

We consider tandem queues which have a general arrival process. The queueing system consists of s (s ≧ 2) single-server service stations and the servers have exponential service-time distributions. Firstly we give a new proof for the fact that the departure process does not depend on the particular allocation of the servers to the stations. Secondly, considering the service rates, we prove that the departure process becomes stochastically faster as the homogeneity of the servers increases in the sense of a given condition. It turns out that, given the sum of the service rates, the departure process is stochastically fastest in the case where the servers are homogeneous.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

1997 ◽  
Vol 29 (2) ◽  
pp. 545-566 ◽  
Author(s):  
Naoto Miyoshi ◽  
Toshiharu Hasegawa
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Single Server ◽  
Single Server Queues ◽  
The Family ◽  
Service Disciplines ◽  
Preemptive Resume Priority ◽  
Queueing Processes ◽  
Strongly Consistent ◽  
General Service

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Optimal admission control for a single-server loss queue

2004 ◽  
Vol 41 (02) ◽  
pp. 535-546 ◽  
Author(s):  
Kyle Y. Lin ◽  
Sheldon M. Ross
Keyword(s):  
Admission Control ◽  
Time Horizon ◽  
Queueing System ◽  
Single Server ◽  
Sufficient Condition ◽  
Infinite Time ◽  
Discounted Cost ◽  
Time Period ◽  
Service Distribution ◽  
General Service

This paper presents a single-server loss queueing system where customers arrive according to a Poisson process. Upon arrival, the customer presents itself to a gatekeeper who has to decide whether to admit the customer into the system without knowing the busy–idle status of the server. There is a cost if the gatekeeper blocks a customer, and a larger cost if an admitted customer finds the server busy and therefore has to leave the system. The goal of the gatekeeper is to minimize the total expected discounted cost on an infinite time horizon. In the case of an exponential service distribution, we show that a threshold-type policy—block for a time period following each admission and then admit the next customer—is optimal. For general service distributions, we show that a threshold-type policy need not be optimal; we then present a sufficient condition for the existence of an optimal threshold-type policy.

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