Nishant Modak

Posted on

# Nobody likes to wait in a Queue

Nobody likes to wait in a queue. Almost everyone in a queue at immigration or in a road traffic has considered

• What if I move to the other queue? Thats going faster
• Why haven't they added more servers / units / lanes to service?
• This is just the bad time of the day. Should have started early.

Its a science! These things can be answered by formulas and you can study these systems formally.

The mathematical field of studying queues is called Queueing Theory.

## Queueing Theory 101

### Key Concepts

• Arrivals
How things arrive? Stream, Batch
Is there a normal arrival distribution?
Are the arrival times finite / infinite?

• Service
Kind of resources needed to service
How long does it take ?
Number of servers available
How many can be serviced?
Parallel / Serial?
Single / Multiple Queues
Preemption (Priority)

• Queue Characteristics
Balking (people/things don't join, if queue is long)
Reneging (queue too long, leave mid way)
Jockeying (switch queue)
Finite / Infinite (queue lengths)

### Questions we are interested in

1. How long does a customer (*request) have to wait
2. What is the probability of customer having to wait longer
3. Average length of queue
4. Expected utilisation of the server at any given point

#### To Decide

1. Is it worthwhile to improve on service times
2. ‘Auto Scale!’
3. Should we introduce priorities

### Little's Law

L = ƛW

ƛ = Arrival Rate
W = Waiting times
L = Total being serviced

Presentation

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