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Stochastic processes in networks of queues with exponential service times and only one class of customers

Ferreira, Manuel Alberto M.
Fonte: Hikari, Ltd Publicador: Hikari, Ltd
Tipo: Artigo de Revista Científica
Publicado em //2014 ENG
Relevância na Pesquisa
125.99%
Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are exponentially distributed and there is only one class of customers.

Networks of queues models with several classes of customers and exponential service times

Ferreira, Manuel Alberto M.
Fonte: Hikari, Ltd Publicador: Hikari, Ltd
Tipo: Artigo de Revista Científica
Publicado em //2015 ENG
Relevância na Pesquisa
96.03%
The main target of this paper is to present the Markov chain C that, not giving explicitly the queue lengths stationary probabilities, has the necessary information to its determination for open networks of queues with several classes of customers and exponential service times, allowing to overcome ingeniously this problem. The situation for closed networks, in the same conditions, much easier is also presented.

Tail asymptotics for monotone-separable networks

Lelarge, Marc
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.8%
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with i.i.d. driving sequences and the $GI /GI /1/1$ queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.; Comment: 15 pages, shortened version, case of (max,plus)-networks handled in a separate paper