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  • 1
    Electronic Resource
    Electronic Resource
    Some analytical results for congestion in subscriber line modules (1992)
    Springer
    Queueing systems 10 (1992), S. 381-402 
    Details
    ISSN: 1572-9443
    Keywords: Asymptotic behaviours ; diffusion approximations ; iterative algorithms ; retrial queues ; Subscriber Line Modules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In modern telephone exchanges, subscriber lines are usually connected to the so-called subscriber line modules. These modules serve both incoming and outgoing traffic. An important difference between these two types of calls lies in the fact that in the case of blocking due to all channels busy in the module, outgoing calls can be queued whereas incoming calls get busy signal and must be re-initiated in order to establish the required connection. The corresponding queueing model was discussed recently by Lederman, but only the model with losses has been studied analytically. In the present contribution, we study the model which takes into account subscriber retrials and investigate some of its properties such as existence of stationary regime, derive explicit formulas for the system characteristics, limit theorems for systems under high repetition intensity of blocked calls and limit theorems for systems under heavy traffic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193327
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  • 2
    Electronic Resource
    Electronic Resource
    TheM/G/1 retrial queue with the server subject to starting failures (1994)
    Springer
    Queueing systems 16 (1994), S. 83-96 
    Details
    ISSN: 1572-9443
    Keywords: Probability generating functions ; retrial queues ; steady state ; server vacations ; server setup times ; stochastic decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we study a retrial queueing model with the server subject to starting failures. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system in steady state. We show that the general stochastic decomposition law forM/G/1 vacation models also holds for the present system. Finally, we demonstrate that a few well known queueing models are special cases of the present model and discuss various interpretations of the stochastic decomposition law when applied to each of these special cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158950
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  • 3
    Electronic Resource
    Electronic Resource
    A survey on retrial queues (1987)
    Springer
    Queueing systems 2 (1987), S. 201-233 
    Details
    ISSN: 1572-9443
    Keywords: Imbedded Markov chain ; retrial queues ; stochastic decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Queueing systems in which arriving customers who find all servers and waiting positions (if any) occupied may retry for service after a period of time are called retrial queues or queues with repeated orders. Retrial queues have been widely used to model many problems in telephone switching systems, telecommunication networks, computer networks and computer systems. In this paper, we discuss some important retrial queueing models and present their major analytic results and the techniques used. Our concentration is mainly on single-server queueing models. Multi-server queueing models are briefly discussed, and interested readers are referred to the original papers for details. We also discuss the stochastic decomposition property which commonly holds in retrial queues and the relationship between the retrial queue and the queue with server vacations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158899
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  • 4
    Electronic Resource
    Electronic Resource
    On the steady-state queue size distribution of the discrete-timeGeo/G/1 queue with repeated customers (1995)
    Springer
    Queueing systems 21 (1995), S. 199-215 
    Details
    ISSN: 1572-9443
    Keywords: Discrete-time queues ; generating functions ; recursive computation ; retrial queues ; stochastic decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we study the steady-state queue size distribution of the discrete-timeGeo/G/1 retrial queue. We derive analytic formulas for the probability generating function of the number of customers in the system in steady-state. It is shown that the stochastic decomposition law holds for theGeo/G/1 retrial queue. Recursive formulas for the steady-state probabilities are developed. Computations based on these recursive formulas are numerically stable because the recursions involve only nonnegative terms. Since the regularGeo/G/1 queue is a special case of theGeo/G/1 retrial queue, the recursive formulas can also be used to compute the steady-state queue size distribution of the regularGeo/G/1 queue. Furthermore, it is shown that a continuous-timeM/G/1 retrial queue can be approximated by a discrete-timeGeo/G/1 retrial queue by dividing the time into small intervals of equal length and the approximation approaches the exact when the length of the interval tends to zero. This relationship allows us to apply the recursive formulas derived in this paper to compute the approximate steady-state queue size distribution of the continuous-timeM/G/1 retrial queue and the regularM/G/1 queue.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158581
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