Function Reference: qnos

Function File: [U, R, Q, X] = qnos (lambda, S, V)
Function File: [U, R, Q, X] = qnos (lambda, S, V, m)

Analyze open, single class BCMP queueing networks with K service centers.

This function works for a subset of BCMP single-class open networks satisfying the following properties:

  • The allowed service disciplines at network nodes are: FCFS, PS, LCFS-PR, IS (infinite server);
  • Service times are exponentially distributed and load-independent;
  • Center k can consist of m(k) ≥ 1 identical servers.
  • Routing is load-independent

INPUTS

lambda

Overall external arrival rate (lambda>0).

S(k)

average service time at center k (S(k)>0).

V(k)

average number of visits to center k (V(k) ≥ 0).

m(k)

number of servers at center i. If m(k) < 1, enter k is a delay center (IS); otherwise it is a regular queueing center with m(k) servers. Default is m(k) = 1 for all k.

OUTPUTS

U(k)

If k is a queueing center, U(k) is the utilization of center k. If k is an IS node, then U(k) is the traffic intensity defined as X(k)*S(k).

R(k)

center k average response time.

Q(k)

average number of requests at center k.

X(k)

center k throughput.

REFERENCES

  • G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, Wiley, 1998

See also: qnopen, qnclosed, qnosvisits

Example: 1

  

 lambda = 3;
 V = [16 7 8];
 S = [0.01 0.02 0.03];
 [U R Q X] = qnos( lambda, S, V );
 R_s = dot(R,V) # System response time
 N = sum(Q) # Average number in system

R_s = 1.4062
N = 4.2186