A Comparative Numerical Study of the Spectral Theory Approach of Nishimura and the Roots Method Based on the Analysis of BDMMAP/G/1 Queue

Table 4

Distribution of stationary probability at arbitrary epoch using CGG method for deterministic service time distribution.

												Tail probability ()
0
	1	0.002811	0.016898	0.054698	0.047333	0.014415	0.023149	0.001694	0.000382	0.001168	0.001622	0.164170	0.041843
2	0.001795	0.008742	0.021327	0.022088	0.009515	0.017742	0.001806	0.000739	0.001822	0.002387	0.087964	0.038314
3	0.001015	0.005005	0.011847	0.012207	0.005651	0.011572	0.001687	0.000897	0.002406	0.003131	0.055420	0.035081
4	0.000573	0.003182	0.008287	0.008159	0.003570	0.008109	0.001463	0.000905	0.002680	0.003661	0.040588	0.032122
5	0.000349	0.002275	0.006573	0.006242	0.002566	0.006273	0.001266	0.000846	0.002733	0.003903	0.033025	0.029412
6	0.000239	0.001796	0.005581	0.005188	0.002045	0.005216	0.001107	0.000772	0.002656	0.003918	0.028518	0.026931
7	0.000183	0.001515	0.004914	0.004513	0.001735	0.004526	0.000982	0.000701	0.002516	0.003790	0.025376	0.024659
8	0.000151	0.001329	0.004407	0.004021	0.001524	0.004022	0.000882	0.000638	0.002350	0.003586	0.022911	0.022579
9	0.000131	0.001190	0.003992	0.003629	0.001364	0.003622	0.000797	0.000582	0.002177	0.003348	0.020832	0.020674
10	0.000117	0.001077	0.003634	0.003296	0.001233	0.003285	0.000725	0.000531	0.002007	0.003101	0.019007	0.018930
11	0.000106	0.000981	0.003317	0.003005	0.001121	0.002991	0.000661	0.000486	0.001845	0.002859	0.017371	0.017333
12	0.000096	0.000895	0.003032	0.002744	0.001023	0.002731	0.000603	0.000444	0.001693	0.002628	0.015890	0.015871
13	0.000088	0.000819	0.002773	0.002509	0.000934	0.002496	0.000551	0.000406	0.001553	0.002412	0.014542	0.014532
14	0.000080	0.000749	0.002538	0.002296	0.000854	0.002283	0.000504	0.000372	0.001423	0.002212	0.013311	0.013306
15	0.000073	0.000685	0.002323	0.002101	0.000782	0.002089	0.000462	0.000341	0.001303	0.002027	0.012186	0.012183
16	0.000067	0.000627	0.002127	0.001923	0.000715	0.001912	0.000423	0.000312	0.001194	0.001857	0.011157	0.011156
17	0.000061	0.000574	0.001947	0.001761	0.000655	0.001750	0.000387	0.000285	0.001093	0.001701	0.010215	0.010214
18	0.000056	0.000526	0.001783	0.001612	0.000600	0.001602	0.000354	0.000261	0.001001	0.001558	0.009353	0.009353
19	0.000051	0.000482	0.001632	0.001476	0.000549	0.001467	0.000324	0.000239	0.000917	0.001426	0.008564	0.008564
20	0.000047	0.000441	0.001494	0.001352	0.000503	0.001343	0.000297	0.000219	0.000839	0.001306	0.007841	0.007841
21	0.000043	0.000404	0.001368	0.001237	0.000460	0.001230	0.000272	0.000201	0.000769	0.001196	0.007180	0.007180
22	0.000039	0.000370	0.001253	0.001133	0.000421	0.001126	0.000249	0.000184	0.000704	0.001095	0.006574	0.006574
23	0.000036	0.000338	0.001147	0.001037	0.000386	0.001031	0.000228	0.000168	0.000644	0.001003	0.006020	0.006020
24	0.000033	0.000310	0.001050	0.000950	0.000353	0.000944	0.000209	0.000154	0.000590	0.000918	0.005512	0.005512
25	0.000030	0.000284	0.000962	0.000870	0.000323	0.000865	0.000191	0.000141	0.000540	0.000841	0.005047	0.005047
30	0.000019	0.000183	0.000619	0.000560	0.000208	0.000556	0.000123	0.000091	0.000348	0.000541	0.003248	0.003248
40	0.000008	0.000076	0.000256	0.000232	0.000086	0.000230	0.000051	0.000038	0.000144	0.000224	0.001345	0.001345
50	0.000003	0.000031	0.000106	0.000096	0.000036	0.000095	0.000021	0.000016	0.000060	0.000093	0.000557	0.000557
100	0.000000	0.000000	0.000001	0.000001	0.000000	0.000001	0.000000	0.000000	0.000001	0.000001	0.000007	0.000007
	0.010175763	0.101757632	0.305272895	0.228954672	0.062442183	0.145698427	0.020814061	0.012808653	0.044830285	0.067245428	1	0.999998