Sojourn times in queuing networks with multiserver modes

1987 ◽  
Vol 24 (02) ◽  
pp. 511-521 ◽  
Author(s):  
R. Schassberger ◽  
H. Daduna
Keyword(s):  
Sojourn Time ◽  
Product Form ◽  
Queuing Networks ◽  
Sojourn Times ◽  
Networks Of Queues ◽  
Sojourn Time Distributions

This paper generalizes previous results for sojourn-time distributions along so-called overtake-free routes in product-form networks of queues.

Sojourn times in queuing networks with multiserver modes

1987 ◽  
Vol 24 (2) ◽  
pp. 511-521 ◽  
Author(s):  
R. Schassberger ◽  
H. Daduna
Keyword(s):  
Sojourn Time ◽  
Product Form ◽  
Queuing Networks ◽  
Sojourn Times ◽  
Networks Of Queues ◽  
Sojourn Time Distributions

This paper generalizes previous results for sojourn-time distributions along so-called overtake-free routes in product-form networks of queues.

A note on sojourn times in queuing networks with multiserver nodes

1990 ◽  
Vol 27 (02) ◽  
pp. 469-474
Author(s):  
Josef Hemker
Keyword(s):  
Time Reversal ◽  
Sojourn Time ◽  
Product Form ◽  
Queuing Networks ◽  
Sojourn Times ◽  
Sojourn Time Distributions

Time-reversal arguments can be used to re-derive (and slightly generalize) previous results for sojourn-time distributions in product-form queuing networks.

A note on sojourn times in queuing networks with multiserver nodes

1990 ◽  
Vol 27 (2) ◽  
pp. 469-474 ◽  
Author(s):  
Josef Hemker
Keyword(s):  
Time Reversal ◽  
Sojourn Time ◽  
Product Form ◽  
Queuing Networks ◽  
Sojourn Times ◽  
Sojourn Time Distributions

Time-reversal arguments can be used to re-derive (and slightly generalize) previous results for sojourn-time distributions in product-form queuing networks.

scholarly journals A Technique for Computing Sojourn Times in Large Networks of Interacting Queues

1993 ◽  
Vol 7 (4) ◽  
pp. 441-464 ◽  
Author(s):  
V. Anantharam ◽  
M. Benchekroun
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Sojourn Time ◽  
Asymptotic Limit ◽  
Large Networks ◽  
Sojourn Times ◽  
Sojourn Time Distributions

Consider a large number of interacting queues with symmetric interactions. In the asymptotic limit, the interactions between any fixed finite subcollection become negligible, and the overall effect of interactions can be replaced by an empirical rate. The evolution of each queue is given by a time inhomogeneous Markov process. This may be considered a technique for writing dynamic Erlang fixed-point equations. We explore this as a tool to approximate sojourn time distributions.

scholarly journals Sojourn times in finite Markov processes

1989 ◽  
Vol 26 (4) ◽  
pp. 744-756 ◽  
Author(s):  
Gerardo Rubino ◽  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Sojourn Time ◽  
Sojourn Times ◽  
Finite State ◽  
Sojourn Time Distributions ◽  
Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

scholarly journals Sojourn times in finite Markov processes

1989 ◽  
Vol 26 (04) ◽  
pp. 744-756 ◽  
Author(s):  
Gerardo Rubino ◽  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Sojourn Time ◽  
Sojourn Times ◽  
Finite State ◽  
Sojourn Time Distributions ◽  
Finite State Space

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues

1984 ◽  
Vol 31 (1) ◽  
pp. 128-133 ◽  
Author(s):  
O. J. Boxma ◽  
F. P. Kelly ◽  
A. G. Konheim
Keyword(s):  
Sojourn Time ◽  
Product Form ◽  
Sojourn Time Distributions

Sojourn times and the overtaking condition in Jacksonian networks

1980 ◽  
Vol 12 (04) ◽  
pp. 1000-1018 ◽  
Author(s):  
J. Walrand ◽  
P. Varaiya
Keyword(s):  
Sojourn Time ◽  
Sojourn Times ◽  
Mutually Independent

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.

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