Analytically Explicit Results for the Distribution of the Number of Customers Served during a Busy Period for Special Cases of the M/G/1 Queue

Table 3

Distribution of the number of customers served during a busy period.

n	Matrix exponential distribution			Chi-square distribution
	, ,			, ,
	3	0.339685			0.220001
	4	0.222371			0.170756
5	0.139825			0.125171
6	0.090430			0.093132
7	0.060262	0.080509		0.070848	0.029218
8	0.041179	0.122977		0.055009	0.052916
9	0.028722	0.130997	0.039195	0.043465	0.066170	0.010648
10	0.020371	0.121409	0.076975	0.034852	0.071365	0.024794
20	0.001091	0.014350	0.033872	0.006110	0.031203	0.044522
50	0.000001	0.000016	0.000054	0.000167	0.001229	0.002577
100	0.000000	0.000000	0.000000	0.000001	0.000011	0.000026
	5.1703	12.0640	15.5109	7.5000	17.5000	22.5000
	35.5201	166.047	266.953	95.625	398.125	118.125
	8.7880	20.5054	26.3641	39.375	91.875	624.375