On Queue-Length Information in a Tandem Queueing System

2020 ◽  
Author(s):  
Jingwei Ji ◽  
Ricky Roet-Green
Keyword(s):  
Queue Length ◽  
Queueing System

scholarly journals An analysis of steady-state distribution in M/M/1 queueing system with balking based on concept of statistical mechanics

2019 ◽  
Author(s):  
IKUO ARIZONO ◽  
Yasuhiko Takemoto
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Queue Length ◽  
Queueing System ◽  
Analysis Model ◽  
Steady State Distribution ◽  
Steady State Analysis ◽  
Extended Analysis ◽  
The Moment ◽  
State Analysis

The phenomenon of balking has been considered frequently in the steady-state analysis of the M/M/1 queueing system. Balking means the phenomenon that a customer who arrives at a queueing system leaves without joining a queue, since he/she is disgusted with the waiting queue length at the moment of his/her arrival. In the traditional studies for the steady-state analysis of the M/M/1 queueing system with balking, it has been typically assumed that the arrival rates obey an inverse proportional function for the waiting queue length. In this study, based on the concept of the statistical mechanics, we have a challenge to extend the traditional steady-state analysis model for the M/M/1 queueing system with balking. As the result, we have defined an extended analysis model for the M/M/1 queueing system under the consideration of the change in the directivity strength of balking. In addition, the procedure for estimating the strength of balking in this analysis model using the observed data in the M/M/1 queueing system has been also constructed.

Analysis of the M x/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (02) ◽  
pp. 476-496
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

Transient solutions for denumerable-state Markov processes

1994 ◽  
Vol 31 (03) ◽  
pp. 635-645
Author(s):  
Guang-Hui Hsu ◽  
Xue-Ming Yuan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Initial Distribution ◽  
Numerical Results ◽  
Transient Solution ◽  
Queue Length Distribution ◽  
Transient Solutions

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

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.

The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System

1969 ◽  
Vol 6 (1) ◽  
pp. 154-161 ◽  
Author(s):  
E.G. Enns
Keyword(s):  
Queue Length ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
List Type ◽  
Type Number ◽  
Distribution Of The Maximum ◽  
Maximum Queue Length ◽  
Number Of Customers

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:1.The duration of the busy period.2.The number of customers served during the busy period.3.The maximum number of customers in the queue during the busy period.

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.

Controlled queues in heavy traffic

1975 ◽  
Vol 7 (3) ◽  
pp. 656-671 ◽  
Author(s):  
John H. Rath
Keyword(s):  
Diffusion Process ◽  
Queue Length ◽  
Queueing System ◽  
Systems Approach ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Control Policy ◽  
Controlled Diffusion ◽  
Controlled Queues

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

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