Two-Dimensional Markov Processes and Their Applications to Memoryless Queues

2013 ◽  
pp. 181-216
Author(s):  
Moshe Haviv
Keyword(s):  
Markov Processes ◽  
Two Dimensional

scholarly journals A compensation approach for two-dimensional Markov processes

1993 ◽  
Vol 25 (4) ◽  
pp. 783-817 ◽  
Author(s):  
I. J. B. F. Adan ◽  
J. Wessels ◽  
W. H. M. Zijm
Keyword(s):  
Random Walks ◽  
Markov Processes ◽  
Infinite Series ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Compensation Approach ◽  
Queueing Processes ◽  
Random Behaviour ◽  
Elegant Solution

Several queueing processes may be modeled as random walks on a multidimensional grid. In this paper the equilibrium distribution for the case of a two-dimensional grid is considered. In previous research it has been shown that for some two-dimensional random walks the equilibrium distribution has the form of an infinite series of products of powers which can be constructed with a compensation procedure. The object of the present paper is to investigate under which conditions such an elegant solution exists and may be found with a compensation approach. The conditions can be easily formulated in terms of the random behaviour in the inner area and the drift on the boundaries.

Extended continued fractions, recurrence relations and two-dimensional Markov processes

1989 ◽  
Vol 21 (2) ◽  
pp. 357-375 ◽  
Author(s):  
C. E. M. Pearce
Keyword(s):  
Markov Processes ◽  
Continued Fractions ◽  
Recurrence Relations ◽  
Equilibrium Distribution ◽  
Linear Recurrence ◽  
Natural State ◽  
Two Dimensional ◽  
State Spaces ◽  
General Order ◽  
Dimension 2

Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.

Extended continued fractions, recurrence relations and two-dimensional Markov processes

1989 ◽  
Vol 21 (02) ◽  
pp. 357-375 ◽  
Author(s):  
C. E. M. Pearce
Keyword(s):  
Markov Processes ◽  
Continued Fractions ◽  
Recurrence Relations ◽  
Equilibrium Distribution ◽  
Linear Recurrence ◽  
Natural State ◽  
Two Dimensional ◽  
State Spaces ◽  
General Order ◽  
Dimension 2

Connections between Markov processes and continued fractions have long been known (see, for example, Good [8]). However the usefulness of extended continued fractions in such a context appears not to have been explored. In this paper a convergence theorem is established for a class of extended continued fractions and used to provide well-behaved solutions for some general order linear recurrence relations such as arise in connection with the equilibrium distribution of state for some Markov processes whose natural state spaces are of dimension 2. Specific application is made to a multiserver version of a queueing problem studied by Neuts and Ramalhoto [13] and to a model proposed by Cohen [5] for repeated call attempts in teletraffic.

Learning the dynamics of two-dimensional stochastic Markov processes

1992 ◽  
Vol 1 (3) ◽  
pp. 311-326 ◽  
Author(s):  
Lisa Borland ◽  
Hermann Haken
Keyword(s):  
Markov Processes ◽  
Two Dimensional

Two-dimensional avalanches as stochastic Markov processes

1993 ◽  
Vol 47 (4) ◽  
pp. R2229-R2232 ◽  
Author(s):  
E. Morales-Gamboa ◽  
J. Lomnitz-Adler ◽  
V. Romero-Rochín ◽  
R. Chicharro-Serra ◽  
R. Peralta-Fabi
Keyword(s):  
Markov Processes ◽  
Two Dimensional

scholarly journals A compensation approach for two-dimensional Markov processes

1993 ◽  
Vol 25 (04) ◽  
pp. 783-817 ◽  
Author(s):  
I. J. B. F. Adan ◽  
J. Wessels ◽  
W. H. M. Zijm
Keyword(s):  
Random Walks ◽  
Markov Processes ◽  
Infinite Series ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Compensation Approach ◽  
Queueing Processes ◽  
Random Behaviour ◽  
Elegant Solution

Several queueing processes may be modeled as random walks on a multidimensional grid. In this paper the equilibrium distribution for the case of a two-dimensional grid is considered. In previous research it has been shown that for some two-dimensional random walks the equilibrium distribution has the form of an infinite series of products of powers which can be constructed with a compensation procedure. The object of the present paper is to investigate under which conditions such an elegant solution exists and may be found with a compensation approach. The conditions can be easily formulated in terms of the random behaviour in the inner area and the drift on the boundaries.

scholarly journals Two Dimensional Semi-Stable Markov Processes

1975 ◽  
Vol 3 (3) ◽  
pp. 440-448 ◽  
Author(s):  
Sun-Wah Kiu
Keyword(s):  
Markov Processes ◽  
Two Dimensional

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

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