Product form solutions for discrete-time queueing networks with bursty traffic

2000 ◽  
Vol 36 (17) ◽  
pp. 1512 ◽  
Author(s):  
M.E. Woodward
Keyword(s):  
Discrete Time ◽  
Queueing Networks ◽  
Product Form ◽  
Bursty Traffic

scholarly journals Discrete-time queueing networks with geometric release probabilities

1992 ◽  
Vol 24 (01) ◽  
pp. 229-233
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Discrete Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Time Interval

This note is concerned with the continuing misconception that a discrete-time network of queues, with independent customer routing and the number of arrivals and services in a time interval following geometric and truncated geometric distributions respectively, has a product-form equilibrium distribution.

scholarly journals Discrete-time queueing networks with geometric release probabilities

1992 ◽  
Vol 24 (1) ◽  
pp. 229-233 ◽  
Author(s):  
W. Henderson ◽  
P. G. Taylor
Keyword(s):  
Discrete Time ◽  
Queueing Networks ◽  
Equilibrium Distribution ◽  
Product Form ◽  
Time Interval

This note is concerned with the continuing misconception that a discrete-time network of queues, with independent customer routing and the number of arrivals and services in a time interval following geometric and truncated geometric distributions respectively, has a product-form equilibrium distribution.

scholarly journals On the quasi-stationary distribution for queueing networks with defective routing

1997 ◽  
Vol 38 (4) ◽  
pp. 454-463 ◽  
Author(s):  
Richard J. Boucherie
Keyword(s):  
Markov Chains ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Queueing Networks ◽  
Product Form ◽  
Stationary Distributions ◽  
Absorbing States ◽  
Quasi Stationary Distribution

AbstractThis note introduces quasi-local-balance for discrete-time Markov chains with absorbing states. From quasi-local-balance product-form quasi-stationary distributions are derived by analogy with product-form stationary distributions for Markov chains that satisfy local balance.

scholarly journals Networks—B

2021 ◽  
pp. 93-113
Author(s):  
Jean Walrand
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Time Reversal ◽  
Continuous Time ◽  
Queueing Networks ◽  
Product Form ◽  
Continuous Time Markov Chains

AbstractThis chapter provides the derivations of the results in the previous chapter. It also develops the theory of continuous-time Markov chains.Section 6.1 proves the results on the spreading of rumors. Section 6.2 presents the theory of continuous-time Markov chains that are used to model queueing networks, among many other applications. That section explains the relationships between continuous-time and related discrete-time Markov chains. Sections 6.3 and 6.4 prove the results about product-form networks by using a time-reversal argument.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

Sign in / Sign up

Export Citation Format

Share Document