Stationary Single-Server Queuing Processes with a Finite Number of Sources

1959 ◽  
Vol 7 (4) ◽  
pp. 458-467 ◽  
Author(s):  
Gerald Harrison
Keyword(s):  
Finite Number ◽  
Single Server

Queues with semi-Markovian arrivals

1967 ◽  
Vol 4 (02) ◽  
pp. 365-379 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Finite Number ◽  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Interarrival Time ◽  
Single Server ◽  
Queue Size

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.

THE ISRAELI QUEUE WITH INFINITE NUMBER OF GROUPS

2013 ◽  
Vol 28 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Nir Perel ◽  
Uri Yechiali
Keyword(s):  
Finite Number ◽  
Performance Measures ◽  
Infinite Number ◽  
Batch Service ◽  
Single Server ◽  
Polling System ◽  
Priority Class ◽  
Lower Priority ◽  
The One ◽  
Priority Model

The so called “Israeli Queue” is a single server polling system with batch service of an unlimited size, where the next queue to be visited is the one in which the first customer in line has been waiting for the longest time. The case with finite number of queues (groups) was introduced by Boxma, Van der Wal and Yechiali [3]. In this paper we extend the model to the case with a (possibly) infinite number of queues. We analyze the M/M/1, M/M/c, and M/M/1/N—type queues, as well as a priority model with (at most) M high-priority classes and a single lower priority class. In all models we present an extensive probabilistic analysis and calculate key performance measures.

Time dependence of queues with semi-Markovian services

1967 ◽  
Vol 4 (02) ◽  
pp. 356-364 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Finite Number ◽  
Time Dependence ◽  
Service Time ◽  
Queueing System ◽  
Single Server ◽  
Queue Size ◽  
Poisson Input

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

Time dependence of queues with semi-Markovian services

1967 ◽  
Vol 4 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Finite Number ◽  
Time Dependence ◽  
Service Time ◽  
Queueing System ◽  
Single Server ◽  
Queue Size ◽  
Poisson Input

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

scholarly journals OPTIMAL SWITCHING ON AND OFF THE ENTIRE SERVICE CAPACITY OF A PARALLEL QUEUE

2015 ◽  
Vol 29 (4) ◽  
pp. 483-506 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Xiaoxuan Zhang
Keyword(s):  
Linear Programming ◽  
Finite Number ◽  
Optimal Policy ◽  
Average Cost ◽  
Optimization Problem ◽  
System Size ◽  
Single Server ◽  
Service Capacity ◽  
Optimal Switching ◽  
Holding Costs

This paper studies optimal switching on and off of the entire service capacity of an M/M/∞ queue with holding, running and switching costs. The running costs depend only on whether the system is on or off, and the holding costs are linear. The goal is to minimize average costs per unit time. The main result is that an average-cost optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-cost optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-cost optimal.

A single-server queueing system with a finite number of demands

Cybernetics ◽  
1974 ◽  
Vol 8 (3) ◽  
pp. 465-470 ◽  
Author(s):  
A. M. Andronov
Keyword(s):  
Finite Number ◽  
Queueing System ◽  
Single Server

NUMBER OF RETRIALS IN A FINITE SOURCE RETRIAL QUEUE WITH UNRELIABLE SERVER

2014 ◽  
Vol 31 (02) ◽  
pp. 1440005 ◽  
Author(s):  
VELIKA I. DRAGIEVA
Keyword(s):  
Steady State ◽  
Finite Number ◽  
Retrial Queue ◽  
Life Time ◽  
Retrial Queues ◽  
Single Server ◽  
System State ◽  
Finite Source ◽  
Management Optimization ◽  
Continue Investigation

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

Queues with semi-Markovian arrivals

1967 ◽  
Vol 4 (2) ◽  
pp. 365-379 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Finite Number ◽  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Interarrival Time ◽  
Single Server ◽  
Queue Size

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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