Answer:
On average, customer spends approximately 98 min at Little’s Law Firm
Step-by-step explanation:
Given the data in the question;
Arrival rate λ = 6 per 8 hours = 6 / ( 8 × 60 )min = 6 / 480 = 0.0125 per minute
Service rate δ = 1 / 50 min = 0.02 per minute
Standard deviation σ = 20 min
Now,
Utilization rate U = Arrival rate / Service rate
U = 0.0125 / 0.02
Utilization rate = 0.625
Number of people in Queue will be;
⇒ ( (λ² × σ²) + U² ) / ( 2 × ( 1 - U )
we substitute
⇒ ( (0.0125² × 20²) + 0.625² ) / ( 2 × ( 1 - 0.625 )
⇒ ( 0.0625 + 0.390625 ) / ( 2 × 0.375 )
⇒ 0.453125 / 0.75
Number of people in Queue = 0.6042
Now
Wait in the Queue = Number of people in Queue / λ
= 0.6042 / 0.0125 = 48.336
Wait Time in Office = Wait in the Queue + ( 1 / δ )
= 48.336 + ( 1 / 0.02 )
= 48.336 + 50
Wait Time in Office = 98.336 ≈ 98 min
Therefore, On average, customer spends approximately 98 min at Little’s Law Firm
