Mean sojourn times in Markov queueing networks: Little's formula revisited

1983 ◽  
Vol 29 (2) ◽  
pp. 233-241 ◽  
Author(s):  
F. Beutler
Keyword(s):  
Queueing Networks ◽  
Sojourn Times ◽  
Little's Formula

Conditional job-observer property for multitype closed queueing networks

2002 ◽  
Vol 39 (4) ◽  
pp. 865-881 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Cycle Time ◽  
Queueing Networks ◽  
Closed Queueing Networks ◽  
Basic Formula ◽  
Sojourn Times ◽  
Number Of Customers ◽  
Insight Into

For functionals of multitype closed queueing networks, a conditional job-observer property is shown which provides more insight into the classical job-observer property. Applications and examples are given, including the classical job-observer property for the number of customers in a network, a representation of cycle time distributions and a basic formula for sojourn times.

A Method for Approximating the Variance of the Sojourn Times in Star-Shaped Queueing Networks

2008 ◽  
Vol 24 (3) ◽  
pp. 487-501 ◽  
Author(s):  
R. D. van der Mei ◽  
A. R. de Wilde ◽  
S. Bhulai
Keyword(s):  
Queueing Networks ◽  
Sojourn Times

Sojourn Times in Queueing Networks

1982 ◽  
Vol 7 (2) ◽  
pp. 223-244 ◽  
Author(s):  
Benjamin Melamed
Keyword(s):  
Queueing Networks ◽  
Sojourn Times

Conditional expected sojourn times in insensitive queueing systems and networks

1984 ◽  
Vol 16 (4) ◽  
pp. 906-919 ◽  
Author(s):  
Uwe Jansen
Keyword(s):  
Queueing Networks ◽  
Point Processes ◽  
Response Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Main Tool ◽  
Closed Queueing Networks ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Special Cases

We consider queueing systems where the stationary state probabilities are insensitive with respect to the distribution of certain basic random variables such as service requirements, interarrival times, repair times, etc. The conditional expected sojourn times are stated as Radon–Nikodym densities of the stationary distribution at jump points of the queueing system. The conditions are the given values of such basic random variables for which the insensitivity is valid. We use stationary point processes as our main tool. This means that dependences between certain basic random variables are permitted. Conditional expected real service times, conditional mean response times in closed queueing networks, and similar conditional expected values, are dealt with as special cases.

Maxima of sojourn times in acyclic Jackson queueing networks

1997 ◽  
Vol 24 (11) ◽  
pp. 1085-1095 ◽  
Author(s):  
Sungyeol Kang ◽  
Richard F. Serfozo
Keyword(s):  
Queueing Networks ◽  
Sojourn Times

Conditional job-observer property for multitype closed queueing networks

2002 ◽  
Vol 39 (04) ◽  
pp. 865-881 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Cycle Time ◽  
Queueing Networks ◽  
Closed Queueing Networks ◽  
Basic Formula ◽  
Sojourn Times ◽  
Number Of Customers ◽  
Insight Into

For functionals of multitype closed queueing networks, a conditional job-observer property is shown which provides more insight into the classical job-observer property. Applications and examples are given, including the classical job-observer property for the number of customers in a network, a representation of cycle time distributions and a basic formula for sojourn times.

Sojourn times in closed queueing networks

1983 ◽  
Vol 15 (03) ◽  
pp. 638-656 ◽  
Author(s):  
F. P. Kelly ◽  
P. K. Pollett
Keyword(s):  
Free Path ◽  
Queueing Networks ◽  
Joint Distribution ◽  
The State ◽  
Product Form ◽  
Closed Queueing Networks ◽  
Jackson Network ◽  
Simple Representation ◽  
Sojourn Times

This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.

Conditional expected sojourn times in insensitive queueing systems and networks

1984 ◽  
Vol 16 (04) ◽  
pp. 906-919 ◽  
Author(s):  
Uwe Jansen
Keyword(s):  
Queueing Networks ◽  
Point Processes ◽  
Response Times ◽  
Queueing Systems ◽  
Random Variables ◽  
Main Tool ◽  
Closed Queueing Networks ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Special Cases

We consider queueing systems where the stationary state probabilities are insensitive with respect to the distribution of certain basic random variables such as service requirements, interarrival times, repair times, etc. The conditional expected sojourn times are stated as Radon–Nikodym densities of the stationary distribution at jump points of the queueing system. The conditions are the given values of such basic random variables for which the insensitivity is valid. We use stationary point processes as our main tool. This means that dependences between certain basic random variables are permitted. Conditional expected real service times, conditional mean response times in closed queueing networks, and similar conditional expected values, are dealt with as special cases.

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