An airline is planning to open a satellite ticket desk in a new shopping plaza,

Question

An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed by one ticket agent. It is estimated that requests for tickets and information will average 15 per hour, and requests will have a Poissorn distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggests that mean service time should average about three minutes per request. Determine each of the following: a. System utilization b. Percentage of time the server (agent) will be idle. c. The expected number of customers waiting to be served. customers will spend in the system. The probability of no customers in the system and the probability of four customers in the system e.

Explanation / Answer

Following details are to be noted :

Arrival rates for tickets and information = a = 15 / hour

Service rate ( @ 3 minutes/ request ) = S = 60/3 = 20 / hour

= a^2/ S x ( S – a)

= 15 x 15/ 20 x ( 20 – 15 )

= 225/100

= 2.25

= 15/ 20 x ( 20 – 15)+ 1/20 hours

= 3/20 + 1/20 hours

= 4/20 hours

= 4 x 60/20 minutes

= 12 minutes

Probability of 4 customers in the system = ( a/s)^4 x Po = (15/20)^4 x 0.25 = 0.75 x 0.75 x 0.75 x 0.25 = 0.1054

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