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  • 1
    Electronic Resource
    Electronic Resource
    TheGr X n/G n/∞ system: System size (1991)
    Springer
    Queueing systems 8 (1991), S. 323-356 
    Details
    ISSN: 1572-9443
    Keywords: Infinite server ; batch arrival ; Markov renewal input ; customer dependence ; analytical result
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An important property of most infinite server systems is that customers are independent of each other once they enter the system. Though this non-interacting property (NIP) has been instrumental in facilitating excellent results for infinite server systems in the past, the utility of this property has not been fully exploited or even fully recognized. This paper exploits theNIP by investigating a general infinite server system with batch arrivals following a Markov renewal input process. The batch sizes and service times depend on the customer types which are regulated by the Markov renewal process. By conditional approaches, analytical results are obtained for the generating functions and binomial moments of both the continuous time system size and pre-arrival system size. These results extend the previous results on infinite server queues significantly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02412259
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Departures in $$GR^{X{n}} /G_n /\infty $$ (1995)
    Springer
    Queueing systems 19 (1995), S. 399-419 
    Details
    ISSN: 1572-9443
    Keywords: Departures ; infinite server ; batch arrival ; customer dependence ; analytical result
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Departure processes in infinite server queues with non-Poisson arrivals have not received much attention in the past. In this paper, we try to fill this gap by considering the continuous time departure process in a general infinite server system with a Markov renewal batch arrival process ofM different types of customers. By a conditional approach, analytical results are obtained for the generating functions and binomial moments of the departure process. Special cases are discussed, showing that while Poisson arrival processes generate Poisson departures, departure processes are much more complicated with non-Poisson arrivals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01151931
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  • 3
    Electronic Resource
    Electronic Resource
    Queue lengths in the GIX/MR/∞ service system (1996)
    Springer
    Queueing systems 22 (1996), S. 129-144 
    Details
    ISSN: 1572-9443
    Keywords: Infinite server ; batch arrival ; batch service ; analytical results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Service systems with queueing often have both batch arrivals and batch services. This paper focuses on the number of busy servers and waiting customers in theGI X/MR/∞ system. For the number of busy servers, we obtain a recursive relation for the partial binomial moments in terms of matrices and explicit expressions for the marginal binomial moments. Special cases are also discussed to provide a more heuristic understanding of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01159397
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  • 4
    Electronic Resource
    Electronic Resource
    Autocorrelations in infinite server batch arrival queues (1993)
    Springer
    Queueing systems 14 (1993), S. 313-337 
    Details
    ISSN: 1572-9443
    Keywords: Autocorrelation ; estimate ; customer dependence ; batch arrival ; ample service
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper studies an important aspect of queueing theory, autocorrelation properties of system processes. A general infinite server queue with batch arrivals is considered. There areM different types of customers and their arrivals are regulated by a Markov renewal input process. Batch sizes and service times depend on the relevant customer types. With a conditional approach, closed form expressions are obtained for the autocovariance of the continuous time and prearrival system sizes. Some special models are also discussed, giving insights into steady state system behaviour. Autocorrelation functions have a wide range of applications. We highlight one area of application by using autocovariances to derive variances of sample means for a number of special models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158871
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  • 5
    Electronic Resource
    Electronic Resource
    The service system M/M R /∞ with impatient customers (1987)
    Springer
    Queueing systems 2 (1987), S. 363-372 
    Details
    ISSN: 1572-9443
    Keywords: Infinite server ; impatient customers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An infinite server queue is considered where customers have a choice of individual service or batch service. Transient results have been obtained for the first two moments of the system size distribution. Waiting time distribution is important in system evaluation and steady state results are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01150047
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