Function File: [Xl, Xu, Rl, Ru, Ql, Qu] = qncsgb (N, D)

Function File: [Xl, Xu, Rl, Ru, Ql, Qu] = qncsgb (N, S, V)

Function File: [Xl, Xu, Rl, Ru, Ql, Qu] = qncsgb (N, S, V, m)

Function File: [Xl, Xu, Rl, Ru, Ql, Qu] = qncsgb (N, S, V, m, Z)

Compute Geometric Bounds (GB) on system throughput, system response time and server queue lenghts for closed, single-class networks with K service centers and N requests.

INPUTS

N

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

D(k)

service demand of service center k (vector of length K, D(k) ≥ 0).

S(k)

mean service time at center k (vector of length K, S(k) ≥ 0).

V(k)

visit ratio to center k (vector of length K, V(k) ≥ 0).

m(k)

number of servers at center k. This function only supports M/M/1 queues, therefore m must be ones(size(S)).

Z

external delay (think time, Z ≥ 0, scalar). Default is 0.

OUTPUTS

Xl

Xu

Lower and upper bound on the system throughput. If Z>0, these bounds are computed using Geometric Square-root Bounds (GSB). If Z==0, these bounds are computed using Geometric Bounds (GB)

Rl

Ru

Lower and upper bound on the system response time. These bounds are derived from Xl and Xu using Little’s Law: Rl = N / Xu - Z, Ru = N / Xl - Z

Ql(k)

Qu(k)

lower and upper bounds of center K queue length.

REFERENCES

• G. Casale, R. R. Muntz, G. Serazzi, Geometric Bounds: a Non-Iterative Analysis Technique for Closed Queueing Networks, IEEE Transactions on Computers, 57(6):780-794, June 2008. 10.1109/TC.2008.37

In this implementation we set X^+ and X^- as the upper and lower Asymptotic Bounds as computed by the qncsab function, respectively.

Package: queueing