On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (1) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (01) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

Steady state solution of a single-server queue with linear repeated requests

1997 ◽  
Vol 34 (01) ◽  
pp. 223-233 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Steady State ◽  
Hypergeometric Functions ◽  
Queueing Systems ◽  
General Setting ◽  
Steady State Solution ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
Server Queue ◽  
Number Of Customers

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

Steady state solution of a single-server queue with linear repeated requests

1997 ◽  
Vol 34 (1) ◽  
pp. 223-233 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Steady State ◽  
Hypergeometric Functions ◽  
Queueing Systems ◽  
General Setting ◽  
Steady State Solution ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
Server Queue ◽  
Number Of Customers

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

scholarly journals Imbedded Markov chain analysis of single server bulk queues

1964 ◽  
Vol 4 (2) ◽  
pp. 244-263 ◽  
Author(s):  
U. Narayan Bhat
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Arrival Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Chain Analysis ◽  
Special Cases ◽  
Poisson Arrivals ◽  
Negative Exponential

SummaryIn this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.

BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS

2008 ◽  
Vol 22 (3) ◽  
pp. 355-371 ◽  
Author(s):  
Liqiang Liu ◽  
Vidyadhar G. Kulkarni
Keyword(s):  
Steady State ◽  
Single Server ◽  
Impatient Customers ◽  
Operating Characteristics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Numerical Examples ◽  
Exact Analysis ◽  
Analytical Results ◽  
Server System

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.

A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (1) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

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.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (01) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

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