Mathematics: Heyyyy want to help meee? I know you want tooo

Heyyyy want to help meee? I know you want tooo

joelxl101

29.05.2023

1. c

2. f

3. d

Step-by-step explanation:

This type of queuing model is an example of "single-channel, single-phase" process.

However, from the information given:

The inter-arrival rate = 10 customers per hour

Arrival time = 6 minutes

Service time = 5 minutes

∴

utilization = service time/arrival time

= 5/6

Time on queue $T_q = p \times \dfrac{utilization }{1 - utilization} \times \dfrac{Cv_a^2 -Cv_b^2}{2}$

$T_q = 5 \times \dfrac{5/6 }{1 -5/6} \times \dfrac{(2.58^2 -0.75^2)}{2}$

$T_q = 25 \times 3.60945$

$T_q = 90.24 \\ \\ T_q \simeq 90 \ mins$

Thus, customer waiting in the queue line is;

$= \dfrac{T_q}{q} \\ \\ = \dfrac{90}{6} \\ \\ \mathbf{=15}$

Thus, new customers will have to wait in a total time of;

= waiting time + service time

= 90 + 5

= 95 minutes.

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