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contains values of P 0 for selected values of l/ and k. The values provided in the table
correspond to cases where k > l, and hence the service rate is sufficient to process
all arrivals.
Operating Characteristics for the Dome Problem
To illustrate the multiple-channel queuing model, we return to the Dome restaurant
queuing problem. Suppose that management wants to evaluate the desirability of
Table 11.4 Values of P 0 for Multiple-Channel Queues with Poisson Arrivals and
Exponential Service Times
Number of Channels (k)
Ratio l/ 2 3 4 5
0.15 0.8605 0.8607 0.8607 0.8607
0.20 0.8182 0.8187 0.8187 0.8187
0.25 0.7778 0.7788 0.7788 0.7788
0.30 0.7391 0.7407 0.7408 0.7408
0.35 0.7021 0.7046 0.7047 0.7047
0.40 0.6667 0.6701 0.6703 0.6703
0.45 0.6327 0.6373 0.6376 0.6376
0.50 0.6000 0.6061 0.6065 0.6065
0.55 0.5686 0.5763 0.5769 0.5769
0.60 0.5385 0.5479 0.5487 0.5488
0.65 0.5094 0.5209 0.5219 0.5220
0.70 0.4815 0.4952 0.4965 0.4966
0.75 0.4545 0.4706 0.4722 0.4724
0.80 0.4286 0.4472 0.4491 0.4493
0.85 0.4035 0.4248 0.4271 0.4274
0.90 0.3793 0.4035 0.4062 0.4065
0.95 0.3559 0.3831 0.3863 0.3867
1.00 0.3333 0.3636 0.3673 0.3678
1.20 0.2500 0.2941 0.3002 0.3011
1.40 0.1765 0.2360 0.2449 0.2463
1.60 0.1111 0.1872 0.1993 0.2014
1.80 0.0526 0.1460 0.1616 0.1646
2.00 0.1111 0.1304 0.1343
2.20 0.0815 0.1046 0.1094
2.40 0.0562 0.0831 0.0889
2.60 0.0345 0.0651 0.0721
2.80 0.0160 0.0521 0.0581
3.00 0.0377 0.0466
3.20 0.0273 0.0372
3.40 0.0186 0.0293
3.60 0.0113 0.0228
3.80 0.0051 0.0174
4.00 0.0130
4.20 0.0093
4.40 0.0063
4.60 0.0038
4.80 0.0017
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