Mathematical Problems in Engineering / 2011 / Article / Tab 1

Research Article

Upper Bounds on Performance Measures of Heterogeneous 𝑀 / 𝑀 / 𝑐 Queues

Table 1

Maximum errors (in %) in the predictions of the average waiting times in queue for the proposed method and for the traditional homogeneous queue.

Number of serversAllocation strategy
Approximation method FSF RCS SSF

2 0.90 Proposed bounds2.27 1.36 0.77
Homogeneous 4.66 4.764.99
0.75 Proposed bounds 6.91 3.93 1.93
Homogeneous 12.52 13.11 13.49
0.60 Proposed bounds14.08 7.31 3.18
Homogeneous 21.49 22.9523.63

3 0.90 Proposed bounds 4.30 2.52 1.37
Homogeneous 8.42 8.88 8.87
0.75 Proposed bounds13.70 7.40 3.51
Homogeneous 22.62 23.33 23.59
0.60 Proposed bounds29.56 14.64 5.88
Homogeneous 37.97 39.21 39.79

6 0.90 Proposed bounds 6.89 4.70 2.45
Homogeneous 16.37 16.57 17.16
0.75 Proposed bounds23.58 11.82 5.43
Homogeneous 40.41 41.81 42.36
0.60 Proposed bounds62.75 22.64 8.64
Homogeneous 57.97 64.93 65.66

12 0.90 Proposed bounds 8.63 4.35 2.22
Homogeneous 27.48 27.96 28.28
0.75 Proposed bounds31.77 13.69 5.85
Homogeneous 62.09 63.17 63.53
0.60 Proposed bounds99.33 27.06 9.46
Homogeneous 85.53 86.54 86.87

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