scholarly journals A fixed-size batch service queue with vacations

1996 ◽  
Vol 9 (2) ◽  
pp. 205-219 ◽  
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
K. C. Chae
Keyword(s):  
Queue Length ◽  
Decomposition Method ◽  
Batch Service ◽  
Decomposition Techniques ◽  
Fixed Size ◽  
Open Problems ◽  
Multiple Vacation ◽  
Process Decomposition ◽  
Queues With Vacations ◽  
Batch Service Queues

The paper deals with batch service queues with vacations in which customers arrive according to a Poisson process. Decomposition method is used to derive the queue length distributions both for single and multiple vacation cases. The authors look at other decomposition techniques and discuss some related open problems.

A non-exponential queueing system with independent arrivals and batch servicing

1990 ◽  
Vol 27 (02) ◽  
pp. 401-408
Author(s):  
Nico M. Van Dijk ◽  
Eric Smeitink
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Service Systems ◽  
Batch Service ◽  
Repair System ◽  
Theoretical Interest ◽  
Form Expression ◽  
Queue Length Distribution ◽  
Service Times

We study a queueing system with a finite number of input sources. Jobs are individually generated by a source but wait to be served in batches, during which the input of that source is stopped. The service speed of a server depends on the mode of other sources and thus includes interdependencies. The input and service times are allowed to be generally distributed. A classical example is a machine repair system where the machines are subject to shocks causing cumulative damage. A product-form expression is obtained for the steady state joint queue length distribution and shown to be insensitive (i.e. to depend on only mean input and service times). The result is of both practical and theoretical interest as an extension of more standard batch service systems.

scholarly journals Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 979
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj ◽  
Ramdane Hedjar
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Threshold Level ◽  
Tail Probability ◽  
Probability Vector ◽  
Fixed Size ◽  
Markovian Queue ◽  
Entropy Principle ◽  
Service Rates ◽  
Good Agreement

In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or equal to c. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach.

Optimal control of batch service queues

1973 ◽  
Vol 5 (2) ◽  
pp. 340-361 ◽  
Author(s):  
Rajat K. Deb ◽  
Richard F. Serfozo
Keyword(s):  
Decision Process ◽  
Time Horizon ◽  
Optimal Level ◽  
Batch Size ◽  
Batch Service ◽  
Service Capacity ◽  
Infinite Time ◽  
Discounted Cost ◽  
Markov Decision ◽  
Batch Service Queues

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

scholarly journals Process decomposition method with reachable vector.

1992 ◽  
Vol 25 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Delin Qu ◽  
Dengwen Sun ◽  
Masaaki Muraki ◽  
Toyohiko Hayakawa
Keyword(s):  
Decomposition Method ◽  
Process Decomposition

ON TRUNCATION PROPERTIES OF FINITE-BUFFER QUEUES AND QUEUEING NETWORKS

2000 ◽  
Vol 14 (4) ◽  
pp. 409-423 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Queueing Networks ◽  
Additional Condition ◽  
Queueing Systems ◽  
Batch Service ◽  
Single Server ◽  
Finite Buffer ◽  
Finite Buffers ◽  
Batch Service Queues

We show that several truncation properties of queueing systems are consequences of a simple property of censored stochastic processes. We first consider a discrete-time stochastic process and show that its censored process has a truncated stationary distribution. When the stochastic process has continuous time, we present a similar result under the additional condition that the process is locally balanced. We apply these results to single-server batch arrival batch service queues with finite buffers and queueing networks with finite buffers and batch movements, and extend the well-known results on truncation properties of the MX/G/1/k queues and queueing networks with jump-over blocking.

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