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 𝑀/𝑀/𝑐 queue.

Number of servers			Allocation strategy
𝑐	𝜌	Approximation method	FSF	RCS	SSF
2	0.90	Proposed bounds	2.27	1.36	0.77
		Homogeneous 𝑀/𝑀/𝑐	4.66	4.76	4.99
	0.75	Proposed bounds	6.91	3.93	1.93
		Homogeneous 𝑀/𝑀/𝑐	12.52	13.11	13.49
	0.60	Proposed bounds	14.08	7.31	3.18
		Homogeneous 𝑀/𝑀/𝑐	21.49	22.95	23.63
3	0.90	Proposed bounds	4.30	2.52	1.37
		Homogeneous 𝑀/𝑀/𝑐	8.42	8.88	8.87
	0.75	Proposed bounds	13.70	7.40	3.51
		Homogeneous 𝑀/𝑀/𝑐	22.62	23.33	23.59
	0.60	Proposed bounds	29.56	14.64	5.88
		Homogeneous 𝑀/𝑀/𝑐	37.97	39.21	39.79
6	0.90	Proposed bounds	6.89	4.70	2.45
		Homogeneous 𝑀/𝑀/𝑐	16.37	16.57	17.16
	0.75	Proposed bounds	23.58	11.82	5.43
		Homogeneous 𝑀/𝑀/𝑐	40.41	41.81	42.36
	0.60	Proposed bounds	62.75	22.64	8.64
		Homogeneous 𝑀/𝑀/𝑐	57.97	64.93	65.66
12	0.90	Proposed bounds	8.63	4.35	2.22
		Homogeneous 𝑀/𝑀/𝑐	27.48	27.96	28.28
	0.75	Proposed bounds	31.77	13.69	5.85
		Homogeneous 𝑀/𝑀/𝑐	62.09	63.17	63.53
	0.60	Proposed bounds	99.33	27.06	9.46
		Homogeneous 𝑀/𝑀/𝑐	85.53	86.54	86.87