Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts

1987 ◽  
Vol 24 (2) ◽  
pp. 486-494 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Steady State ◽  
Generating Functions ◽  
Explicit Formulas ◽  
Steady State Probabilities

In this paper we study the M/M/2/2 queue with repeated attempts. It is shown that the part generating functions of the steady state probabilities can be expressed in of generalized hypergeometric unctions.

Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts

1987 ◽  
Vol 24 (02) ◽  
pp. 486-494 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Steady State ◽  
Generating Functions ◽  
Explicit Formulas ◽  
Steady State Probabilities

In this paper we study the M/M/2/2 queue with repeated attempts. It is shown that the part generating functions of the steady state probabilities can be expressed in of generalized hypergeometric unctions.

The steady state of a multi-server mixed queue

1973 ◽  
Vol 5 (03) ◽  
pp. 614-631 ◽  
Author(s):  
N. B. Slater ◽  
T. C. T. Kotiah
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Generating Functions ◽  
Queueing System ◽  
Linear Equations ◽  
Weighted Sum ◽  
System Of Linear Equations ◽  
Different Types ◽  
Multi Server ◽  
Steady State Probabilities

In a multi-server queueing system in which the customers are of several different types, it is useful to define states which specify the types of customers being served as well as the total number present. Analogies with some problems in statistical mechanics are found fruitful. Certain generating functions are defined in such a way that they satisfy a system of linear equations. Solution of the associated eigenvector problem shows that the steady-state probabilities for states in which all the servers are busy can be represented by a weighted sum of geometric probabilities.

scholarly journals Markov chains with quasitoeplitz transition matrix: applications

1990 ◽  
Vol 3 (2) ◽  
pp. 141-152
Author(s):  
A. M. Dukhovny
Keyword(s):  
Steady State ◽  
Markov Chains ◽  
Generating Functions ◽  
Transition Matrix ◽  
Queueing Systems ◽  
Warm Up ◽  
Hitting Probabilities ◽  
Steady State Probabilities ◽  
Transient And Steady State

Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ( “warm-up,” “switch at threshold” etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and MI/G/1 types with arbitrary random sizes of arriving and departing groups are studied.

scholarly journals Rhombic alternative tableaux, assemblees of permutations, and the ASEP

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Olya Mandelshtam ◽  
Xavier Viennot
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Generating Functions ◽  
Finite Lattice ◽  
One Dimensional ◽  
Open Boundaries ◽  
Bijective Proof ◽  
Insertion Algorithm ◽  
International Audience ◽  
Steady State Probabilities

International audience In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice with open boundaries, and theparametersα,β, andqdescribe the hopping probabilities. The rhombic alternative tableaux are enumerated by theLah numbers, which also enumerate certainassembl ́ees of permutations. We describe a bijection between the rhombicalternative tableaux and these assembl ́ees. We also provide an insertion algorithm that gives a weight generatingfunction for the assemb ́ees. Combined, these results give a bijective proof for the weight generating function for therhombic alternative tableaux.

scholarly journals Markov chains with quasitoeplitz transition matrix

1989 ◽  
Vol 2 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Alexander M. Dukhovny
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Markov Chains ◽  
Generating Functions ◽  
Transition Matrix ◽  
Queueing Systems ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Steady State Probabilities ◽  
Transient And Steady State

This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories) with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.

scholarly journals M/M/1 Queueing system with Customer Balking and Reneging

2019 ◽  
Vol 8 (9) ◽  
pp. 2636-2646
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
Probability Generating Functions ◽  
Multiple Vacation ◽  
Steady State Probabilities ◽  
Explicit Expressions

This paper deals with an M/M/1 queueing system with customer balking and reneging. Balking and reneging of the customers are assumed to occur due to non-availability of the server during vacation and breakdown periods. Steady state probabilities for both the single and multiple vacation scenarios are obtained by employing probability generating functions. We evaluate the explicit expressions for various performance measures of the queueing system.

The steady state of a multi-server mixed queue

1973 ◽  
Vol 5 (3) ◽  
pp. 614-631 ◽  
Author(s):  
N. B. Slater ◽  
T. C. T. Kotiah
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Generating Functions ◽  
Queueing System ◽  
Linear Equations ◽  
Weighted Sum ◽  
System Of Linear Equations ◽  
Different Types ◽  
Multi Server ◽  
Steady State Probabilities

In a multi-server queueing system in which the customers are of several different types, it is useful to define states which specify the types of customers being served as well as the total number present. Analogies with some problems in statistical mechanics are found fruitful. Certain generating functions are defined in such a way that they satisfy a system of linear equations. Solution of the associated eigenvector problem shows that the steady-state probabilities for states in which all the servers are busy can be represented by a weighted sum of geometric probabilities.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Liouville quantum gravity — holography, JT and matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Thomas G. Mertens ◽  
Gustavo J. Turiaci
Keyword(s):  
String Theory ◽  
Generating Functions ◽  
Preliminary Evidence ◽  
Quantum Deformation ◽  
Dilaton Gravity ◽  
Continuum Approach ◽  
Genus Zero ◽  
Explicit Formulas ◽  
Liouville Gravity ◽  
The Continuum

Abstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

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