Table 13. Queuing value Route ρ = ( λ s... | Emerald Publishing

Table 13.

Queuing value

Route	ρ = $(\frac{λ}{s μ})$ (S = t)	P₀ (1 − ρ)	L_s $(\frac{ρ}{1 - ρ})$	L_q $(L_{S} - \frac{λ}{μ})$	W_q $(\frac{L_{q}}{λ})$	W_S $(\frac{L_{S}}{λ})$	Q	Queue formation
R₁	0.85	0.15	5.66	4.81	0.44	0.51	−1.19	No
R₂	1	Queue rate = maximum queue capacity					0	No
R₃	0.75	0.25	3	2.25	0.25	0.33	−3.75	No
R₄	0.93	0.07	13.28	12.35	0.95	1.02	6.35	Yes
R₅	0.81	0.19	4.26	3.45	0.38	0.47	−2.55	No
R₆	1.16	Arrival rate > Service rate, i.e. Queue rate > Maximum queue capacity					10.24	Yes
R₇	1	Queue rate = Maximum queue capacity					0	No
R₈	0.88	0.12	7.33	6.45	0.40	0.45	0.45	Yes
R₉	0.94	0.06	15.67	14.73	0.98	1.04	8.73	Yes
Remarks: Zero in ‘Q’ indicates that no queue formation up to the value and negative sign indicates that no queue formed in the particular route

Route	ρ = $(\frac{λ}{s μ})$ (S = t)	P₀ (1 − ρ)	L_s $(\frac{ρ}{1 - ρ})$	L_q $(L_{S} - \frac{λ}{μ})$	W_q $(\frac{L_{q}}{λ})$	W_S $(\frac{L_{S}}{λ})$	Q	Queue formation
R₁	0.85	0.15	5.66	4.81	0.44	0.51	−1.19	No
R₂	1	Queue rate = maximum queue capacity					0	No
R₃	0.75	0.25	3	2.25	0.25	0.33	−3.75	No
R₄	0.93	0.07	13.28	12.35	0.95	1.02	6.35	Yes
R₅	0.81	0.19	4.26	3.45	0.38	0.47	−2.55	No
R₆	1.16	Arrival rate > Service rate, i.e. Queue rate > Maximum queue capacity					10.24	Yes
R₇	1	Queue rate = Maximum queue capacity					0	No
R₈	0.88	0.12	7.33	6.45	0.40	0.45	0.45	Yes
R₉	0.94	0.06	15.67	14.73	0.98	1.04	8.73	Yes
Remarks: Zero in ‘Q’ indicates that no queue formation up to the value and negative sign indicates that no queue formed in the particular route