QUEUING

Queuing• Queues are a part of life and waiting to be

served is never really pleasant.• The longer people wait the less likely they

are to want to come back to your shop.• Businesses need to manage their queues

so that waiting time are not too long – but also that server time is maximised.

• The convention that operates in queues is FIFO.

Assumptions

• As the customer is finished being served, the next customer is instantly ready to be served.

• That there are no breakdowns/price checks/eftpos transactions.

• The person being served is NOT included in the queue length.

• The book sometimes does this and sometimes doesn’t we NEVER include the person being served.

Single Server Queues• With this there is only one server and they keep working

at a constant pace.• As one person is finished with – the next person is

served straight away.• Arrival Time is when the customer lines up to be served.• Service Time is how long each customer is served for.• Start / Finish Service – are the times that the person

starts being attended to and then when they leave.• Customer Waiting Time is the Start Service – Arrival

Time – in minutes.• Server Idle Time is the time that the server is not serving

anyone – normally occurs in multi server situations.• Queue Length is the number of people waiting to be

served at the start of a service period.

• This would be the case for a small deli or even an ATM.

• The queue length does not include the person being served.

A shop opens at 9:00a am and it takes 4 minutes to serve every customer, and customers arrive every 3 minutes. Draw up a table for the first 7 customers and calculate the average waiting time and server idle time.

Multi Server Queues

• Business need to be aware of customer satisfaction, and waiting in a queue too long may make customers to take their business elsewhere.

• One way to cut down customer waiting time is to have more than one server.

• In the following example there are two servers with standard arrival and service times.

A shop opens at 9:00 am and has 2 servers and it takes 4 minutes to serve every customer, and customers arrive every 3 minutes. Draw up a table for the first 7 customers and calculate the average waiting time and server idle time.

Average waiting time = total waiting time / number of customers -> 0/7 = 0 minutes

Percentage Idle time = (total idle time/time studied) * 100/number of servers= (13/22) * 100/2 = 29.55%

• The problem with this simplistic set up is that the customer waiting time has reduced to 0, but the idle time of the servers has increases to over 29%.

• A business needs to balance waiting time and server idle time. It is expensive having a worker wait for customers – so often other tasks are taken on by the servers.

Example

• A large store opens at 9:00 with 4 people waiting. The shop has 2 servers who serve all the time. Arrive every 2 minutes - service time 5 minutes.

• Design a table and a graph to show this situation. (do this for a 20 minute period)

• What is the average customer waiting time – is this appropriate?

Average waiting time = 25/20 = 2.27 minutes

Average queue length = 13/11 = 1.18 people in queue

Service time (avg) / number of servers = 5/2 = 2.5 mins per server.Not a good model – it takes longer to serve a customer than they are waiting for – so the queue will get longer.