Function Reference: qncsaba

Function File: [Xl, Xu, Rl, Ru] = qncsaba (N, D)
Function File: [Xl, Xu, Rl, Ru] = qncsaba (N, S, V)
Function File: [Xl, Xu, Rl, Ru] = qncsaba (N, S, V, m)
Function File: [Xl, Xu, Rl, Ru] = qncsaba (N, S, V, m, Z)

Compute Asymptotic Bounds for the system throughput and response time of closed, single-class networks with K service centers.

Single-server and infinite-server nodes are supported. Multiple-server nodes and general load-dependent servers are not supported.

INPUTS

N

number of requests in the system (scalar, N>0).

D(k)

service demand at center k (D(k) ≥ 0).

S(k)

mean 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 k (if m is a scalar, all centers have that number of servers). If m(k) < 1, center k is a delay center (IS); if m(k) = 1, center k is a M/M/1-FCFS server. This function does not support multiple-server nodes. Default is 1.

Z

External delay (scalar, Z ≥ 0). Default is 0.

OUTPUTS

Xl
Xu

Lower and upper bounds on the system throughput.

Rl
Ru

Lower and upper bounds on the system response time.

REFERENCES

  • Edward D. Lazowska, John Zahorjan, G. Scott Graham, and Kenneth C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models, Prentice Hall, 1984. http://www.cs.washington.edu/homes/lazowska/qsp/. In particular, see section 5.2 ("Asymptotic Bounds").

See also: qncmaba

Example: 1

  

 S = [10 7 5 4];
 NN = 50;
 Xl = Xu = Xmva = zeros(1,NN);
 for n=1:NN
   [Xl(n) Xu(n)] = qncsaba(n,S);
   [na na na X] = qncsmva(n,S,ones(size(S)));
   Xmva(n) = X(1);
 endfor
 plot(1:NN, Xl, ":b", "linewidth", 2, ...
      1:NN, Xu, ":b;ABA;", "linewidth", 2, ...
      1:NN, Xmva, "k;MVA;", "linewidth", 2);
 xlabel("N. of requests");
 ylim([0, 0.15]);
 title("System throughput"); legend("boxoff");
 legend("location", "northeast");
plotted figure