Queuing Theory in the Labor Market

What is queuing theory?

• Mathematical analysis of queues and waiting times in stochastic systems

• Often used to analyze production and service processes exhibiting random variability in market demand

• Queues arise when short term demand for service > service capacity

Brief History of Queuing Theory

• First instance of queuing theory in 1917 by Agner Erlang

– Modeled number of telephone calls arriving at Copenhagen Telephone Exchange using a Poisson process

– Solved two important queuing models M/D/1 and M/D/k

Applications of Queuing Theory• ER: Patients arrive either by ambulance or on their own

accord. One doctor is always on duty, but the more patients there are, the longer the queue is. How many more doctors should be hired?

• Banks: Initially there is one ATM per branch, leading to long queues and customer dissatisfaction. How many ATMs should be added to optimize customer service but also keep expenses down?

Calling population

Arrival process Queue Queue

DisciplineService

mechanism

Served jobs exit system

input queuing system

Important Parameters

• Calling population – the population from which customers + jobs originate. Most commonly infinite.

• Arrival process – determines how, when, where customers + jobs arrive in the system. Interarrival times are important

Important Parameters

• Queue – number of queues, location, effect on customer behavior, max size

• Queue discipline – principle by which jobs in the queue are served, such as FIFO, LIFO, SPT, EDD, etc.

• Service mechanism – number of servers and service time

Multiple vs. Single Line Queue

Arrival time distribution

Number of serversService time

distribution

A/B/CTerminology of Models