Answered step by step
Verified Expert Solution
Question
1 Approved Answer
A call centre has 2 trainees to deal with customer enquires. The centre has a dispatcher to direct the calls automatically to one of the
A call centre has trainees to deal with customer enquires. The centre has a dispatcher to
direct the calls automatically to one of the trainees. The dispatcher does not contain any
queueing facilities. At each trainees terminal, there is a facility to queue up to calls. The
queueing network at the call centre is depicted in Figure The centre receives on average lambda queries per hour. The arrivals can be modelled by using
the Poisson distribution.
When a query arrives at the dispatcher, it will send the query to Trainee with a probability of p and to Trainee with a probability of p Note that the dispatcher does not
communicate with the trainees terminals, so it is possible that the dispatcher sends a query
to a terminal that has a full queue. You can assume that the dispatcher takes a negligible
time to perform its work and no queries will be dropped at the dispatcher.
Nominally, Trainee can complete or service on average queries per hour. This service
rate applies when the number of customers waiting in their queue is or less. However, when
there are customers waiting in the queue, Trainee feels the pressure of the full queue
and their service rate slows down to
u where
u Trainee performs in exactly the
same way except that their service rate is and their service rate when their queue is full
is
u where
u You can assume all the service times are exponentially distributed and
independent of each other.
When a query arrives at a staffs terminal, it will be answered straight away if the staff is
not busy. Otherwise, the terminal will place the call in its queue if the queue is not full. If a
call arrives when the queue is full, then the call is rejected.Answer the following question:Assuming that p lambda
u and
u determine
the mean waiting time of the queries that have not been rejected by the call centre.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started