Impact of Behavioral Factors on Performance of Multi-Server Queueing Systems

Production and Operations Management ◽

10.1111/poms.12883 ◽

2018 ◽

Vol 27 (8) ◽

pp. 1553-1573 ◽

Cited By ~ 5

Author(s):

Hung T. Do ◽

Masha Shunko ◽

Marilyn T. Lucas ◽

David C. Novak

Keyword(s):

Queueing Systems ◽

Behavioral Factors ◽

Multi Server

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Zero Queueing for Multi-Server Jobs

Proceedings of the ACM on Measurement and Analysis of Computing Systems ◽

10.1145/3447385 ◽

2021 ◽

Vol 5 (1) ◽

pp. 1-25

Author(s):

Weina Wang ◽

Qiaomin Xie ◽

Mor Harchol-Balter

Keyword(s):

Cloud Computing ◽

Stability Region ◽

Transient Analysis ◽

Queueing Systems ◽

Sufficient Conditions ◽

Hard Problem ◽

Queueing Model ◽

Multiple Servers ◽

First Results ◽

Multi Server

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

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Matrix-geometric solution of multi-server queueing systems with Bernoulli scheduled modified vacation and retention of reneged customers: A meta-heuristic approach

Quality Technology & Quantitative Management ◽

10.1080/16843703.2020.1755088 ◽

2020 ◽

pp. 1-28

Author(s):

Chandra Shekhar ◽

Shreekant Varshney ◽

Amit Kumar

Keyword(s):

Queueing Systems ◽

Heuristic Approach ◽

Matrix Geometric Solution ◽

Retention Of Reneged Customers ◽

Multi Server

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Comparing multi-server queues with finite waiting rooms, II: Different numbers of servers

Advances in Applied Probability ◽

10.1017/s0001867800032626 ◽

1979 ◽

Vol 11 (02) ◽

pp. 448-455 ◽

Cited By ~ 3

Author(s):

David Sonderman

Keyword(s):

Probability Space ◽

Queueing Systems ◽

Stochastic Order ◽

Sample Path ◽

System Size ◽

Waiting Room ◽

Virtual Waiting Time ◽

Number Of Customers ◽

Multi Server ◽

Quantities Of Interest

We compare two queueing systems with identical general arrival streams, but different numbers of servers, different waiting room capacities, and stochastically ordered service time distributions. Under appropriate conditions, it is possible to construct two new systems on the same probability space so that the new systems are probabilistically equivalent to the original systems and each sample path of the stochastic process representing system size in one system lies entirely below the corresponding sample path in the other system. This construction implies stochastic order for these processes and many associated quantities of interest, such as a busy period, the number of customers lost in any interval, and the virtual waiting time.

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Comparing multi-server queues with finite waiting rooms, I: Same number of servers

Advances in Applied Probability ◽

10.2307/1426848 ◽

1979 ◽

Vol 11 (2) ◽

pp. 439-447 ◽

Cited By ~ 34

Author(s):

David Sonderman

Keyword(s):

Queueing Systems ◽

Stochastic Comparisons ◽

Waiting Room ◽

Service Times ◽

Interarrival Times ◽

Multi Server

We compare two queueing systems with the same number of servers that differ by having stochastically ordered service times and/or interarrival times as well as different waiting room capacities. We establish comparisons for the sequences of actual-arrival and departure epochs, and demonstrate by counterexample that many stochastic comparisons possible with infinite waiting rooms no longer hold with finite waiting rooms.

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