Whenever I have to discuss Queueing theory in the class I am excited. Queueing was a very favourite topic in my PG class, because it was taught by none other than late Prof. BLN Sastry at Goa Govt Engg College.. Click here for my earlier writing on simple queueing systems ..
Queueing theory is a study of how queues form, how they function and why they malfunction.
Here are top 30+ concepts in Queueing Theory explained in simple terms:
1. Queue: A line of people, tasks, or objects waiting for service. Think of it as a line at a bank or a supermarket checkout.
2. Server: The person or machine that provides the service. In our bank example, it's the teller.
3. Arrival Rate (λ): How fast new customers or tasks are joining the queue. For instance, 5 customers per minute.
4. Service Rate (μ): How fast the server can serve customers. For example, 3 customers per minute.
5. Utilization (ρ): The ratio of the arrival rate to the service rate, showing how busy the server is. If it’s 1, the server is fully occupied.
6. Queue Length: The number of customers or tasks waiting in line. The longer the queue, the longer the wait.
7. Waiting Time: The time a customer or task spends in the queue before being served.
8. Little's Law: A fundamental formula that connects the average number in the system (L), the arrival rate (λ), and the average time in the system (W). It states that \(L = λW\).
9. Single Server Queue (M/M/1): A model where there’s one server, and arrivals and service times follow a specific pattern (Poisson for arrivals, exponential for service times).
10. Multi-Server Queue (M/M/c): Similar to the single server queue, but with multiple servers.
11. Poisson Process: A way to describe random arrivals of customers or tasks over time. If customers arrive at a steady average rate, the actual arrival times are random but predictable in pattern.
12. Exponential Distribution: Describes the time between events (like arrivals or service completions) in a Poisson process. It’s useful because it has a "memoryless" property, meaning the probability of an event happening next doesn't depend on how much time has already passed.
13. Queue Discipline: The rule that determines who gets served next. The most common is FIFO (First In, First Out), but others include LIFO (Last In, First Out) or priority-based.
14. Steady State: A condition where the arrival rate equals the service rate, and the system's characteristics (like average queue length) remain constant over time.
15. Balking: When customers decide not to join the queue because it’s too long.
16. Reneging: When customers leave the queue because they’ve waited too long without being served.
17. Jockeying: When customers switch between queues in the hope of being served faster.
18. Throughput: The rate at which customers are served and leave the system.
19. Blocking: When a queue is full, and no new customers can join until space becomes available.
20. Service Time Distribution: The probability distribution that describes how long it takes to serve customers. It can be exponential, deterministic, or follow other patterns.
21. Markov Chains: A mathematical system that undergoes transitions from one state to another, used to model queues where the next state only depends on the current state.
22. Birth-Death Process: A type of Markov process that models the arrivals (births) and departures (deaths) in a queue.
23. Traffic Intensity: Another term for utilization (ρ), showing how heavily the server is being used.
24. Queueing Network: A system of interconnected queues where customers or tasks move from one queue to another.
25. Kendall's Notation: A shorthand way of describing the characteristics of a queueing model, A/B/C:D/E/F, like M/M/1: G/N/inf or M/G/1. A - arriving rate, B - service rate, C - no. of servers, D - service discipline FCFS (General) etc, E - waiting population, fixed or infinite , F - calling population, fixed or infinite ..
26. G/G/1 Queue: A general queue model where the arrival and service times can follow any distribution.
27. Arrival Process: Describes how customers or tasks arrive at the queue, whether at a constant rate, randomly, or in bursts.
28. Departure Process: Describes how customers or tasks leave the queue after being served.
29. Stochastic Process: A process that involves randomness, used to model the uncertainty in arrival and service times.
30. Queue Stability: A condition where the queue doesn’t grow indefinitely, meaning the system can handle the incoming tasks without becoming overloaded.
31. Steady state: "steady-state" refer to the condition where the system's performance metrics do not change over time
32. Infinite queue - A queue with no limit on the number of customers that can wait
33. State-dependent service - The service rate depends on the number of customers in the system
34. Queue stability - The condition where the arrival rate is less than the service rate, preventing the queue from growing indefinitely
These concepts form the backbone of Queueing Theory, which helps in understanding and optimizing systems where waiting lines occur, from customer service to computer networks.
(This list has been compiled with help from public domain AI systems)
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