Question

Alpha Taxi & Hauling Company has seven cabs stationed at the railway station. The company has determined that during the late‐evening hours on weeknights, customers request cabs at a rate that follows the Poisson distribution with a mean of 6.6 per hour. Service time is exponential with a mean of 50 minutes per customer. Assume that there is one customer per cab. Using multi‐server model find the following: • Average queue length Lq • Average waiting time Wq • Utilization factor ρ • Probability that there are no customers in the system P0

Answer 1

Solution:

Given: Arrival rate =6.6 per hour

Service time =1 customer per trip/(50 minutes per trip/60 minutes per hour)=1.2 customers per hour per cab

Number of cabs,m=7

1) Average queue length Lq

=/=6.6/1.2=5.5

From the above table, we have Lq=1.674 and Po=0.003 for /=5.5 and m=7(check the highlight part in above table)

2) Average waiting time Wq

Wq=Lq/=1.674/6.6=0.254 hours

3)Utilization factor ρ

ρ= /m=6.6/(7*1.2)=0.786

4)Probability that there are no customers in the system Po

From the above table, we have got Po=0.003