Question

a queue will not form if capacity exceeds demand and inter arrival times are variable

True or False?

Answer 1

False.

If capacity exceeds demand then a queue will not form. However, if customers do not arrive in a consistent pattern i.e. the average arrival rate is more than the average capacity then a queue will form.

e.g. Average capacity in a bank with one teller window is 4 people per hour and we assume this rate does not change.

If the customers arrive at fixed intervals - 1 every 15 mins or more, then there will be no queue at any time during the day as

average arrival rate of 3-4 persons per hour (demand) =<  average processing rate of 4 people per hour (capacity)

and so a queue will not form.

However, if the inter arrival times are variable i.e. first customer arrives at 1.01, and second at 1.05 and third at 1.06, then there will be a queue formed in that hour as the bank teller processes one request at a time.

hourly capacity (4)   >= hourly demand (3) , however due to the variable inter arrival times there will be a queue until 1.30 when the third person's request is taken up by the bank teller.

Queues/delays are the result of a disparity between current demand and current capacity available to meet that demand. Variability in the timing can create these temporary queues.

Another example is a healthcare clinic where patients can walk in without appointments whenever they choose. This can lead to unpredictable demand and create queues at certain times of the day, while others are relatively free with minimal to no queues.

(Green)

References :

Green, Linda. Queuing theory and modeling. Columbia Business School Faculty Research paper.