scholarly journals A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

2017 ◽  
Author(s):  
Eline De Cuypere ◽  
Koen De Turck ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Series Expansion ◽  
Maclaurin Series ◽  
Phase Type ◽  
Distributed Service ◽  
Service Times

scholarly journals Detailed state probability distribution of infinite servers queues with phase-type distributed service times

2015 ◽  
Vol 3 (1) ◽  
pp. 29
Author(s):  
Ivan Mura
Keyword(s):  
Probability Distribution ◽  
State Probability ◽  
Phase Type ◽  
Distributed Service ◽  
Service Times

ONTARE. REVISTA DE INVESTIGACIÓN DE LA FACULTAD DE INGENIERÍAEste documento presenta un análisis detallado de la cola M/PH/∞, la cual permite determinar de una forma analítica, tanto para un estado transitorio como para uno estacionario, la distribución de probabilidad de los clientes en las distintas fases del servicio. El análisis se basa en la correspondencia que se puede encontrar entre el proceso estocástico que representa el número de clientes en servicioen las diferentes fases de la distribución de PH, y en un proceso estocástico que representa la evolución del número de clientes en los nodos de una red Jackson en la que todos los centros de servicio son colas M/M/∞.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

Behavior of Coefficients of Inverses of α-Spiral Functions

1986 ◽  
Vol 38 (6) ◽  
pp. 1329-1337 ◽  
Author(s):  
Richard J. Libera ◽  
Eligiusz J. Złotkiewicz
Keyword(s):  
Unit Disk ◽  
Series Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Maclaurin Series ◽  
Koebe Function ◽  
One To One ◽  
Image Position

If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form(1.1)then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.(1.1)serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .

On closed ring queueing networks

1992 ◽  
Vol 29 (04) ◽  
pp. 979-995 ◽  
Author(s):  
Nicholas Bambos
Keyword(s):  
Steady State ◽  
Queueing Networks ◽  
Circulation Time ◽  
Ring Networks ◽  
Closed Queueing Networks ◽  
Closed Ring ◽  
Distributed Service ◽  
Service Times ◽  
Special Case ◽  
General Networks

In this paper we first study ring structured closed queueing networks with distinguishable jobs. Under assumptions of periodicity and ergodicity of the service times, essentially the most general, it is shown that the limits defining the average flows of the jobs exist almost surely, and methods for their estimation by simulation are given. However, it turns out that the values of the flows depend on the initial positions of the jobs, due to the emergence of distinct persistent blocking modes. The effect of these modes on the behavior of general networks with queueing loops is examined. For independent and identically distributed service times, conditions are specified for the network to asymptotically approach a steady state at large times. Finally, we study the special case of ring networks with indistinguishable items and stationary and ergodic service times. It is shown that as the number of jobs in the network increases towards infinity, the average circulation time converges to the maximum of the expectations of the service times.

Overflow processes for multiserver queues with finite waiting room

1984 ◽  
Vol 16 (1) ◽  
pp. 8-8
Author(s):  
Jos H. A. De Smit
Keyword(s):  
Renewal Process ◽  
Numerical Results ◽  
Markov Renewal Process ◽  
Waiting Room ◽  
Multiserver Queues ◽  
Phase Type ◽  
Service Times ◽  
Overflow Process ◽  
Explicit Expressions

The overflow process of the multiserver queue with phase-type service times and finite waiting room is a Markov renewal process. The solution for this process is obtained. If the service times are exponential the overflow process reduces to a renewal process. For the latter case explicit expressions and numerical results are given.

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