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

Table 3

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

		𝑃𝑏	𝑃𝑤𝑣	𝐿𝑞	𝐿.𝑅.	𝑓
𝜇=2.5	𝑏𝑖=1−(𝑖/𝐾^2)	0.207206	0.792794	0.943660	0.313380	100.225
	𝑏𝑖=1/(𝑖+1)	0.009290	0.990710	0.252221	0.674025	86.5458
	𝑏𝑖=𝑒^−𝑖	0.000502	0.999498	0.151711	0.740087	84.6936
𝜇=3.5	𝑏𝑖=1−(𝑖/𝐾^2)	0.137534	0.862466	0.793431	0.264904	113.985
	𝑏𝑖=1/(𝑖+1)	0.006559	0.993441	0.248745	0.671253	104.431
	𝑏𝑖=𝑒^−𝑖	0.000362	0.999637	0.151550	0.739925	102.688
𝜇=2.5	𝛼=0.2	0.252143	0.747857	1.101570	0.254461	103.584
	𝛼=0.5	0.144430	0.855570	0.746728	0.399321	96.1614
	𝛼=0.8	0.088249	0.911750	0.577965	0.484742	92.7966
𝜇=3.5	𝛼=0.2	0.163313	0.836687	0.878758	0.204519	115.514
	𝛼=0.5	0.099092	0.900908	0.668530	0.358484	111.798
	𝛼=0.8	0.062491	0.937509	0.542701	0.455723	109.625
𝜇=2.5	𝜙=0.9	0.199081	0.800919	0.951578	0.315933	100.449
	𝜙=1.1	0.204683	0.795317	0.946113	0.314170	100.295
	𝜙=1.4	0.211783	0.788217	0.939225	0.31195	100.100
𝜇=3.5	𝜙=0.9	0.131773	0.868227	0.807812	0.269538	114.391
	𝜙=1.1	0.135742	0.864258	0.797890	0.266340	114.111
	𝜙=1.4	0.140790	0.859209	0.785357	0.262303	113.757