Optimal dynamic scheduling of a general class of parallel-processing queueing systems

In this paper we develop policies for scheduling dynamically arriving jobs to a broad class of parallel-processing queueing systems. We show that in heavy traffic the policies asymptotically minimize a measure of the expected system backlog, which we call system work. Our results yield succinct, closed-form expressions for optimal system work in heavy traffic.

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Optimal dynamic scheduling of a general class of parallel-processing queueing systems

Advances in Applied Probability ◽

10.1239/aap/1035228211 ◽

1998 ◽

Vol 30 (4) ◽

pp. 1130-1156 ◽

Cited By ~ 3

Author(s):

Noah Gans ◽

Garrett van Ryzin

Keyword(s):

Parallel Processing ◽

Closed Form ◽

General Class ◽

Dynamic Scheduling ◽

Broad Class ◽

Heavy Traffic ◽

Queueing Systems ◽

Optimal System ◽

Call System ◽

Optimal Dynamic

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Scheduling and stability aspects of a general class of parallel processing systems

Advances in Applied Probability ◽

10.2307/1427501 ◽

1993 ◽

Vol 25 (1) ◽

pp. 176-202 ◽

Cited By ~ 15

Author(s):

Nicholas Bambos ◽

Jean Walrand

Keyword(s):

Asymptotic Behavior ◽

Parallel Processing ◽

General Class ◽

Processing Time ◽

Arrival Time ◽

System Designer ◽

Scheduling Policy ◽

Concurrent Processing ◽

Random Flow ◽

Random Amount

In this paper we study the following general class of concurrent processing systems. There are several different classes of processors (servers) and many identical processors within each class. There is also a continuous random flow of jobs, arriving for processing at the system. Each job needs to engage concurrently several processors from various classes in order to be processed. After acquiring the needed processors the job begins to be executed. Processing is done non-preemptively, lasts for a random amount of time, and then all the processors are released simultaneously. Each job is specified by its arrival time, its processing time, and the list of processors that it needs to access simultaneously. The random flow (sequence) of jobs has a stationary and ergodic structure. There are several possible policies for scheduling the jobs on the processors for execution; it is up to the system designer to choose the scheduling policy to achieve certain objectives.We focus on the effect that the choice of scheduling policy has on the asymptotic behavior of the system at large times and especially on its stability, under general stationary and ergocic input flows.

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On a tandem queueing model with identical service times at both counters, II

Advances in Applied Probability ◽

10.2307/1426959 ◽

1979 ◽

Vol 11 (3) ◽

pp. 644-659 ◽

Cited By ~ 12

Author(s):

O. J. Boxma

Keyword(s):

Heavy Traffic ◽

Queueing Systems ◽

Single Server ◽

Service Time Distribution ◽

In Series ◽

Mean And Variance ◽

Queues In Series ◽

The Mean ◽

Service Times ◽

Practical Implications

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

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Asymptotic Transformations of q-Series

Canadian Journal of Mathematics ◽

10.4153/cjm-1998-022-x ◽

1998 ◽

Vol 50 (2) ◽

pp. 412-425 ◽

Cited By ~ 2

Author(s):

Richard J. McIntosh

Keyword(s):

Asymptotic Expansion ◽

Closed Form ◽

Asymptotic Expansions ◽

General Class ◽

Theta Functions ◽

Mock Theta Functions

AbstractFor the q–series we construct a companion q–series such that the asymptotic expansions of their logarithms as q → 1– differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new q–hypergeometric identity. We give an asymptotic expansion of a general class of q–series containing some of Ramanujan's mock theta functions and Selberg's identities.

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