What are the main characteristics of the queue?
Population source
Number of resources (servers)
Arrival & service patterns
Queue discipline
What are the options for the potential number of customers?
Finite-source situation
Infinite-source situation
What is a finite-source situation?
Potential number of customers is limited e.g. repairman responsible for x number of machines
What is an infinite-source situation?
The potential number of customers greatly exceeds system capacity e.g. amusement centres
What are the different channels of a system?
Single-server system and multiserver system
What are phases in a queueing system?
e.g. theme park, people go from one attraction to another. Each attraction constitutes a separate phase where queues can form
What is the distribution of arrival rate and service rate?
Poisson distribution for arrival and service rate
Negative exponential distribution for interarrival and service time
What are the most common queue discipline?
FIFO (first-in-first-out) e.g. stores
LIFO (last-in-first-out) e.g. washing dishes and unloading trucks
Some are neither e.g. emergency room
What are the assumptions of a single-server single-line single-phase system?
- Customers are patient
- Customers arrivals follow a Poisson distribution mean arrival rate of lambda, exponential distribution average 1/lambda
- Customer service rate follow a Poisson distribution mean arrival rate of mu, exponential distribution average 1/mu
- queue discipline is FIIFO
What does rho mean?
The average utilization of the system
What does L mean?
Average number of customers in the system
What does Lq mean?
Average number of customers waiting in queue
What does W mean?
The average time spent in the system, including serivce
What does Wq mean?
The average time spent in queue
What does Pn mean?
The probability that n customers are in the service system at a given time
What extra assumption is there for the single-line, multiple server, single phase model?
All servers (s) are identical and have the same mu
What does s mean?
Number of servers
What are functional areas affected by waiting line decisions?
Accounting e.g. overstaffing
Marketing e.g. response time of service
Purchasing e.g. capital equipment capable of achieving the proposed service rate
Operations e.g. employee skill
What type of changes can one make to the different elements of the waiting line system?
Customer arrival rates e.g. discount during nonpeak hours
Number and type of service facilities e.g. self-service checkout systems, number of cashiers, cash-only
Changing the number of phases e.g. Splitting task up between different servers (specialization)
Server efficiency e.g. grocery bagger or extra scanners
Changing priority rules e.g. multilane models (express lanes)
System
group of objects that are joined together in some regular interaction or interdependence towards the accomplishment of some purpose
Model validity
Making sure the conclusions you draw from the model are valid
