Stepwise explicit solution for the joint distribution of queue length of a MAP single-server service queueing system with splitting and varying batch size delayed-feedback

2016 ◽  
Vol 9 (1) ◽  
pp. 39
Author(s):  
Aliakbar Montazer Haghighi ◽  
Dimitar P. Mishev
Keyword(s):  
Explicit Solution ◽  
Queue Length ◽  
Joint Distribution ◽  
Queueing System ◽  
Delayed Feedback ◽  
Batch Size ◽  
Single Server

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.

Single-server Poisson queueing system with splitting and delayed-feedback: Part I

2011 ◽  
Vol 3 (1) ◽  
pp. 1 ◽  
Author(s):  
Aliakbar Montazer Haghighi ◽  
Stefanka S. Chukova ◽  
Dimitar P. Mishev
Keyword(s):  
Queueing System ◽  
Delayed Feedback ◽  
Single Server

scholarly journals A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

1993 ◽  
Vol 6 (4) ◽  
pp. 359-384 ◽  
Author(s):  
David C. R. Muh
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Numerical Examples ◽  
Queueing Process ◽  
Poisson Input ◽  
Service Delay ◽  
Start Up ◽  
Bulk Arrival

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r(≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥r). Two cases, with N≤R and N≥R, are studied.The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.

scholarly journals MX/G/1 Vacation Queueing System with Two Types of Repair facilities and Server Timeout

2019 ◽  
Vol 8 (9) ◽  
pp. 2040-2043
Keyword(s):  
Size Distribution ◽  
Exponential Distribution ◽  
Service Time ◽  
Queueing System ◽  
Batch Size ◽  
Single Server ◽  
Poisson Arrivals ◽  
Server Failure ◽  
System Length ◽  
General Service

We consider a single server vacation queue with two types of repair facilities and server timeout. Here customers are in compound Poisson arrivals with general service time and the lifetime of the server follows an exponential distribution. The server find if the system is empty, then he will wait until the time ‘c’. At this time if no one customer arrives into the system, then the server takes vacation otherwise the server commence the service to the arrived customers exhaustively. If the system had broken down immediately, it is sent for repair. Here server failure can be rectified in two case types of repair facilities, case1, as failure happens during customer being served willstays in service facility with a probability of 1-q to complete the remaining service and in case2 it opts for new service also who joins in the head of the queue with probability q. Obtained an expression for the expected system length for different batch size distribution and also numerical results are shown

Estimation of traffic intensity from queue length data in a deterministic single server queueing system

2021 ◽  
pp. 113693
Author(s):  
Saroja Kumar Singh ◽  
Sarat Kumar Acharya ◽  
Frederico R.B. Cruz ◽  
Roberto C. Quinino
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Single Server ◽  
Traffic Intensity ◽  
Length Data

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 (01) ◽  
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 On some queue length controlled stochastic processes

1990 ◽  
Vol 3 (4) ◽  
pp. 227-244 ◽  
Author(s):  
Lev Abolnikov ◽  
Jewgeni E. Dshalalow ◽  
Alexander M. Dukhovny
Keyword(s):  
Continuous Time ◽  
Queue Length ◽  
Invariant Probability Measure ◽  
Time Parameter ◽  
Batch Size ◽  
Single Server ◽  
Input Output ◽  
Time Service ◽  
Queueing Processes ◽  
Embedded Process

The authors study the input, output and queueing processes in a general controlled single-server bulk queueing system. It is supposed that inter-arrival time, service time, batch size of arriving units and the capacity of the server depend on the queue length.The authors establish an ergodicity criterion for both the queueing process with continuous time parameter and the embedded process, study their transient and steady state behavior and prove ergodic theorems for some functionals of the input, output and queueing processes. The following results are obtained: Invariant probability measure of the embedded process, stationary distribution of the process with continuous time parameter, expected value of a busy period, rates of input and output processes and the relative speed of convergence of the expected queue length. Various examples (including an optimization problem) illustrate methods developed in the paper.

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