Queueing
Kendall notation, then the M/M/1 queue end to end: utilisation, stability, mean number of customers, time in system and waiting time, Little's law, and a service that clogs up.
- 27 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
- Understand
A few cards from the deck
Kendall notation: what is it?
Show the answer
The A/B/c notation of a queue: the arrival distribution (A), the service-time distribution (B) and the number of servers (c).
M means "memoryless" (Poisson arrivals, exponential service): M/M/3 has three servers and one queue. D denotes a fixed service time.
What does the notation M/M/3 describe?
- Poisson arrivals, exponential services, three servers
- Three separate queues in front of a single shared server
- A queue whose capacity is limited to three customers present
- Three customer classes, each served in its own queue
Show the answer
Poisson arrivals, exponential services, three servers
The third symbol is the number of servers. A limited capacity is written in fourth position, for example M/M/1/K.
In a stable M/M/1 queue, utilisation is ρ = … and the mean number of customers in the system is L = ….
Show the answer
In a stable M/M/1 queue, utilisation is ρ = λ/μ and the mean number of customers in the system is L = ρ/(1 − ρ).
L blows up as ρ approaches 1: at ρ = 0.5 there is 1 customer, at 0.9 there are 9, at 0.99 there are 99.
M/M/1 queue: what is it?
Show the answer
A single-server queue where arrivals follow a Poisson process of rate λ and service times follow an exponential distribution of rate μ.
This is the basic model: it yields closed formulas for waiting, which serve as a benchmark for more complex systems.