Essentially, the problem of Queuing is concerned with:
- Average waiting times
- The average length of the queue
- The number of service points (channels) there should be
- The cost of servicing the queue compared to cost of reducing waiting times
There are two main approaches to working out the solution:
- Queuing theory formulae
Queuing theory formulae can be complicated but are normally used in preference to simulation especially in simple situations.
Let’s take an everyday example, production staff queuing to collect stock from the company stores
So let’s run some numbers assuming the average number of production employees to be served every hour is 12 and we take 3 alternative service rates – 24, 18, 15 per hour, what is the probability of having to queue.
At 24 its 12/24 = 0.5 and the average number of staff in the queue will be 0.5/1-0.5 = 1 employee
At 18 its 12/18 = 0.67 and the average number of staff in the queue will be 0.67/1-0.67 = 2 staff
At 15 its 12/15 = 0.8 and the average number of staff in the queue will be 0.8/1-0.8 = 4 staff
The next stage is to work out the cost of servicing the production team quicker compared to the cost of a faster stores service to reduce queuing
If the production staff cost £20 per hour, based on a 6 hour day that’s £120 per day, that means based on the above the cost will be £120, £240 or £480 for queuing.
If the cost of a faster store man or faster servicing rate is less than the queuing cost then it’s worth investing to reduce the queuing cost.