The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations

Table 2

Queue length distributions at random slots for 𝑎=4, 𝑝=0.3, 𝜇_𝑣=0.4, 𝜇_𝑏=0.6, and 𝜃=0.7.

𝑛	𝜋𝑛,0	𝜋𝑛,1	𝑛	𝜋𝑛,0	𝜋𝑛,1
0	0.6092	0	0	0.4265	0
1	0.0394	0.263	1	0.0654	0.3313
2	0.0024	0.0623	2	0.0041	0.1319
3	1.51𝐸−04	0.012	3	2.51𝐸−04	0.0277
4	9.37𝐸−06	0.0022	4	1.56𝐸−05	0.0052
5	5.80𝐸−07	3.95𝐸−04	5	9.65𝐸−07	9.39𝐸−04
6	3.60𝐸−08	7.05𝐸−05	6	5.98𝐸−08	1.68𝐸−04
7	2.23𝐸−09	1.26𝐸−05	7	3.70𝐸−09	2.99𝐸−05
8	1.38𝐸−10	2.23𝐸−06	8	2.30𝐸−10	5.33𝐸−06
9	8.56𝐸−12	3.97𝐸−07	9	1.42𝐸−11	9.48𝐸−07
10	5.30𝐸−13	7.07𝐸−08	10	8.81𝐸−13	1.69𝐸−07
11	3.29𝐸−14	1.26𝐸−08	11	5.46𝐸−14	3.00𝐸−08
12	2.04𝐸−15	2.24𝐸−09	12	3.38𝐸−15	5.33𝐸−09
13	1.26𝐸−16	3.98𝐸−10	13	2.10𝐸−16	9.49𝐸−10
14	7.82𝐸−18	7.07𝐸−11	14	1.30𝐸−17	1.69𝐸−10
15	4.84𝐸−19	1.26𝐸−11	15	8.05𝐸−19	3.00𝐸−11
Sum	1		Sum	1

𝐸(𝐿)=0.2597, 𝐸(𝑤_𝑞)=0.8425.