Question

Facts
Most flights are scheduled during early morning or early evening.
Based on their circumstances passengers can require drastically different amounts of time for check-in.
Attendants at the service counters must be able to serve passengers at a higher rate than the arrival rate of those passengers.
At some times there are many departing and arriving flights, while at other times there are few flights.
Challenge
To determine how many service counters to keep open.
Busy Period 1		Busy Period 2
Early morning (6:30am to 9:00am)		Early evening (6:00pm to 8:00pm)
Many departing domestic flights		Many departing international flights
Average time between consecutive customer arrivals		Average Service Time
4 minutes for both the morning and evening		8 minutes in the morning
6 minutes in the middle of the day		15 minutes in the evening
		6 minutes in the middle of the day
With multiple service counters, customers can be routed through a single line or dedicated lines for each counter.
You must ensure that customers are not waiting very long and that you're not wasting resources on open counters.
QUESTIONS
During each period:
What is the number of counters that need to be open?
What is the average number of customers in queue and the average waiting time for a customer in the queue before being serviced for check in?
When you need multiple counters open: Do you have one queue for all counters? Do you have dedicated queues for each counter?
What else is being overlooked in the above scenario and your analysis?
How do you ensure that customers are not waiting in line too long before being checked in?
How do you ensure that you don't have too many counters open with no customers at these counters?

Answer 1

The biggest input for the exercise is the average time taken by the airport staff to serve one customer. The time will determine as to how many customers can be served per hour,and appropriate number of counters need to be opened to match the demand, and ensure that the waiting time for an average customer is not too much. Since each resource on the counter adds to the cost of operation, there must be a balance between the cost and waiting time saved.

If one person takes an average time t to serve a customer, the service rate will be 60/t customers per hour

In morning hours where interarrival rate is 60/4 =15 per hour ( lambda) , and service rate is mu, for single counter, the number of customers waiting Lq = 15 x15 / mu (15-mu)

And average waiting time is Lq /lambda.

It can be seen that a single counter system works only till the service rate ( mu) is more than arrival rate lambda. One needs more than one counter when lambda>mu, or it is so close to mu, which will increase the waiting time and line of customer.

Both systems of dedicated queue and a common line can be used. The choice will depend on many factors such as need for dedicated airline counters, counters for senior citizens and priority members, VIP counters etc. If each counter has to do a single operation, the right choice is a common line which will enable the airport authorities to minimise the waiting time.

The point which is being overlooked is the cost of waiting for the customers. It is an important factor in dtermining the optimum number of customers. It can be seen that high waiting time might affect the customers' outlook about an airline or airport itself, and can cause increase in indirect costs, while too many idle resources is also something that is not cost effective. One needs to strike blance between these two factoes while making the optimum decision about the number of counters open..

Note: As per policies, I can answer first 4 parts of a question, Inconvenience is regretted.