“Traffic equations”的意思、由来-开放百科全书

In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual nodes to be determined. Mitrani notes "if the network is stable, the traffic equations are valid and can be solved."^[1]{{rp|125}}

Jackson network

In a Jackson network, the mean arrival rate

at each node i in the network is given by the sum of external arrivals (that is, arrivals from outside the network directly placed onto node i, if any), and internal arrivals from each of the other nodes on the network. If external arrivals at node i have rate

, and the routing matrix^[2] is P, the traffic equations are,^[3] (for i = 1, 2, ..., m)

and there is a unique solution of unknowns

to this equation, so the mean arrival rates at each of the nodes can be determined given knowledge of the external arrival rates

and the matrix P. The matrix I − P is surely non-singular as otherwise in the long run the network would become empty.^[1]

Gordon–Newell network

In a Gordon–Newell network there are no external arrivals, so the traffic equations take the form (for i = 1, 2, ..., m)

Notes

1. ^¹{{Cite book | doi = 10.1017/CBO9781139173087.005| chapter = Queueing networks| title = Probabilistic Modelling| pages = 122| year = 1997| last1 = Mitrani | first1 = I. | isbn = 9781139173087}}
2. ^As explained in the Jackson network article, jobs travel among the nodes following a fixed routing matrix.
3. ^{{Cite book | last = Harrison | first = Peter G. | authorlink = Peter G. Harrison | last2 = Patel | first2 = Naresh M. | title = Performance Modelling of Communication Networks and Computer Architectures | publisher = Addison-Wesley | date = 1992 | isbn = 0-201-54419-9}}{{Page needed|date=December 2010}}