A) Number of agents required to achieve a wait time of 10 minutes or less = 8 agents
B) The number of agents required on duty to reduce cost = 9 agents
<u>Given data : </u>
Arrival rate of customers ( β ) = 220 per hour
Service rate ( mu ) = 60 minutes / 2 minutes = 30 customer per hour
utilization ( rho ) = 220 / 30 ≈ 7
at least 8 server personnel are required for stability of the queue
A<u>) Determine the number of agents required to achieve a wait time of 10 minutes or less per customer</u>
waiting time = 10 - 2 = 8 minutes
number of customers waiting ( ∝ ) = 7 and required server = 8
assuming Lq = 5.2266
Hence the waiting time in line = Lq / arrival rate
= 5.2266 / 220 = 0.0238 hour
= 0.0238 * 60 = 1.428 minutes
Since the waiting time ( 1.428 minutes ) is less than the original waiting time ( 2 minutes ) the number of agents that will achieve a wait time of 10 minutes or less is = 8 agents
<u>B) Determine the number of</u><u> ticket agents</u><u> that should be on duty to minimize cost </u>
salary of ticket agent = £12 per hour
cost of customer waiting in queue = £5 per hour per customer
<em> </em><u>i) When 8 agents are used </u>
waiting time of customers = 0.0238 * 220 = 5.236
waiting cost for customers = 5.236 * 5 = £26.18
employee cost = 8 * 12 = £96
∴ Total cost = 96 + 26.18
= £ 122.18
<u>ii) When 9 agents are used </u>
waiting time for customers = 0.0074 * 220 = 1.628
Wq = 1.6367 / 220 = 0.0074
waiting cost for customers = 1.6367 * 5 = £ 8.1835
assuming Lq = 1.6367
employee cost = 9 * 12 = £ 108
∴ Total cost = 108 + 8.1835 = £ 116.18
From the calculations in ( i ) and ( ii ) the Ideal number of ticket agents that should be on duty to minimize cost should be 9 agents.
Hence we can conclude that A) Number of agents required to achieve a wait time of 10 minutes or less = 8 agents and The number of agents required on duty to reduce cost = 9 agents.
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