Function Reference: qncmcb

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

Compute Composite Bounds (CB) on system throughput and response time for closed multiclass networks.

INPUTS

N(c)

number of class c requests in the system.

D(c, k)

class c service demand at center k (S(c,k) ≥ 0).

S(c, k)

mean service time of class c requests at center k (S(c,k) ≥ 0).

V(c,k)

average number of visits of class c requests to center k (V(c,k) ≥ 0).

OUTPUTS

Xl(c)
Xu(c)

Lower and upper bounds on class c throughput.

Rl(c)
Ru(c)

Lower and upper bounds on class c response time.

REFERENCES

  • Teemu Kerola, The Composite Bound Method (CBM) for Computing Throughput Bounds in Multiple Class Environments, Performance Evaluation Vol. 6, Issue 1, March 1986, DOI 10.1016/0166-5316(86)90002-7. Also available as Technical Report CSD-TR-475, Department of Computer Sciences, Purdue University, mar 13, 1984 (Revised Aug 27, 1984).

Example: 1

  

 S = [10 7 5 4; ...
      5  2 4 6];
 NN=20;
 Xl = Xu = Rl = Ru = Xmva = Rmva = zeros(NN,2);
 for n=1:NN
   N=[n,10];
   [a b c d] = qncmcb(N,S);
   Xl(n,:) = a; Xu(n,:) = b; Rl(n,:) = c; Ru(n,:) = d;
   [U R Q X] = qncmmva(N,S,ones(size(S)));
   Xmva(n,:) = X(:,1)'; Rmva(n,:) = sum(R,2)';
 endfor
 subplot(2,2,1);
 plot(1:NN,Xl(:,1), 1:NN,Xu(:,1), 1:NN,Xmva(:,1), ";MVA;", "linewidth", 2);
 ylim([0, 0.2]);
 title("Class 1 throughput"); legend("boxoff");
 subplot(2,2,2);
 plot(1:NN,Xl(:,2), 1:NN,Xu(:,2), 1:NN,Xmva(:,2), ";MVA;", "linewidth", 2);
 ylim([0, 0.2]);
 title("Class 2 throughput"); legend("boxoff");
 subplot(2,2,3);
 plot(1:NN,Rl(:,1), 1:NN,Ru(:,1), 1:NN,Rmva(:,1), ";MVA;", "linewidth", 2);
 ylim([0, 700]);
 title("Class 1 response time"); legend("location", "northwest"); legend("boxoff");
 subplot(2,2,4);
 plot(1:NN,Rl(:,2), 1:NN,Ru(:,2), 1:NN,Rmva(:,2), ";MVA;", "linewidth", 2);
 ylim([0, 700]);
 title("Class 2 response time"); legend("location", "northwest"); legend("boxoff");
plotted figure