Question

Queuing Theory

Priest Mulcahy currently uses two confessionals with separate rows to serve the needs of his parishioners. Arrivals have been found to be random, at an average rate of 30 people per hour, and service time tends to be random as well, since the number of sins per person can differ greatly. The average time spent in the confessional has been determined to be 3 minutes. It has also been obtained that arrivals are distributed equally between the two lines. Father Mulcahy is considering switching to a single-row system that powers both confessionals. The parent wants to know which system (current or proposed) will lead to the shortest average time in the system for their parishioners.

Answer 1

Given data:

Arrival rate ,

service rate :

no of service station, n = 2.

Current system:

arrival rate is distributing into two line

it means:

arrival rate per system,

Service rate ,

Average time in the system

average time in the system =1/(20-15) = 1/5 = 60/5 min = 12 min.

Average time in cureent system is 12min.

Proposed System

Arrival rate

number of system ,C= 2

Service rate =

P0 = 0.1428

Mean customer in the queue

Lq= 1.9278.

Mean customer in the system ,

Mean time in the system,

Ws= 0.11426 hours = 6.8556 min.

so the proposed system will give shortest average time in the system.