Journal ArticleDOI
Acyclic fork-join queuing networks
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The class of acyclic fork-join queuing networks that arise in various applications, including parallel processing and flexible manufacturing are studied and stability conditions are obtained and upper and lower bounds on the network response times are developed.Abstract:
In this paper the class of acyclic fork-join queuing networks that arise in various applications, including parallel processing and flexible manufacturing are studied. In such queuing networks, a fork describes the simultaneous creation of several new customers, which are sent to different queues. The corresponding join occurs when the services of all these new customers are completed. The evolution equations that govern the behavior of such networks are derived. From this, the stability conditions are obtained and upper and lower bounds on the network response times are developed. These bounds are based on various stochastic ordering principles and on the notion of association of random variables.read more
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Comparison Methods for Queues and Other Stochastic Models
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The fork-join queue and related systems with synchronization constraints: stochastic ordering and computable bounds
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References
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Journal ArticleDOI
Communicating sequential processes
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Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
Book
Statistical Theory of Reliability and Life Testing: Probability Models
Richard E. Barlow,Frank Proschan +1 more
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The stability of a queue with non-independent inter-arrival and service times
TL;DR: In this paper, the authors introduced the concept of subcritical and supercritical queues for series of queues in series and showed that a queue in series is subcritical if E(S 0 − To) > 0, and a queue is supercritical when E(T 0 − T 0) < 0.
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