Optimization of Balking and Reneging Queue with Vacation Interruption under 𝑁-Policy

Table 4

Various performance measures for different balking functions, 𝜂, 𝛼, and 𝜙.

		𝑃𝑏	𝑃𝑤𝑣	𝐿𝑞	𝐿.𝑅.	𝑓
𝜂=2.1	𝑏𝑖=1−(𝑖/𝐾^2)	0.184638	0.815362	0.854715	0.284490	100.713
	𝑏𝑖=1/(𝑖+1)	0.007447	0.992553	0.219831	0.626807	88.2638
	𝑏𝑖=𝑒^−𝑖	0.000393	0.999607	0.132791	0.692532	86.7451
𝜂=2.4	𝑏𝑖=1−(𝑖/𝐾^2)	0.154568	0.845432	0.734459	0.245367	101.815
	𝑏𝑖=1/(𝑖+1)	0.005443	0.994557	0.181192	0.566167	91.1915
	𝑏𝑖=𝑒^−𝑖	0.000279	0.999720	0.110306	0.631206	90.0697
𝜂=2.1	𝛼=0.2	0.226048	0.773952	1.00062	0.231765	103.833
	𝛼=0.5	0.127751	0.872249	0.674428	0.361304	96.9737
	𝛼=0.8	0.077759	0.922240	0.521827	0.438267	93.9284
𝜂=2.4	𝛼=0.2	0.190649	0.809351	0.862265	0.200605	104.563
	𝛼=0.5	0.106066	0.893934	0.578489	0.310791	98.5701
	𝛼=0.8	0.064377	0.935623	0.448454	0.377461	95.9859
𝜂=2.1	𝜙=0.9	0.176926	0.823074	0.859298	0.285968	100.842
	𝜙=1.1	0.182233	0.817767	0.856141	0.284950	100.753
	𝜙=1.4	0.189022	0.810978	0.852124	0.283654	100.640
𝜂=2.4	𝜙=0.9	0.147518	0.852482	0.735379	0.245664	101.841
	𝜙=1.1	0.152358	0.847642	0.734747	0.245460	101.823
	𝜙=1.4	0.158625	0.841375	0.733932	0.245197	101.800