Function File: V = qncsvisits (P)

Function File: V = qncsvisits (P, r)

Compute the mean number of visits to the service centers of a single class, closed network with K service centers.

INPUTS

P(i,j)

probability that a request which completed service at center i is routed to center j (K \times K matrix). For closed networks it must hold that sum(P,2)==1. The routing graph must be strongly connected, meaning that each node must be reachable from every other node.

r

Index of the reference station, r \in {1, …, K}; Default r=1. The traffic equations are solved by imposing the condition V(r) = 1. A request returning to the reference station completes its activity cycle.

OUTPUTS

V(k)

average number of visits to service center k, assuming r as the reference station.

Demonstration 1

 P = [0 0.3 0.7; ...
      1 0   0  ; ...
      1 0   0  ];
 V = qncsvisits(P)

V =

   1.00000   0.30000   0.70000

Package: queueing