--- title: "Queuing system and Kendall's notation" subject: "Telecommunications" chapter: 6 key: "semester_8/telecommunications:queuing-system-kendall" source: https://www.bctengineer.com/q/semester_8/telecommunications/queuing-system-kendall site: BCT Engineering --- # Queuing system and Kendall's notation Telecommunications · Chapter 6: Telephone Traffic - Asked in: 2081 Chaitra, 4+4 marks; 2079 Bhadra, 3+5 marks; 2075 Asoj, 2+6 marks; 2073 Shrawan, 2+6 marks (asked 4 times) - Video: [Kendall's Notation in Queueing Theory | Operation Research in hindi](https://www.youtube.com/watch?v=O3vfHQSAe0s) — Start Practicing - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/queuing-system-kendall - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-6 ## Question What is a queuing system in telecommunication? Explain the characteristics of a simple queuing system in Kendall's notation. ## Short answer A queuing system holds calls in a buffer when all servers are busy, rather than blocking them. Kendall's notation A/B/C/K/N/D describes the arrival process (e.g., M for Poisson), service time distribution, number of servers, system capacity, calling population size, and queue discipline (e.g., FCFS). ## Answer #### Queuing system A **queuing (delay) system** in telecommunication is one in which a call or packet that finds all servers (trunks, registers, processors, links) busy is **not lost but waits** in a queue until a server becomes free. Examples: calls waiting for an operator in a call centre, digits waiting for a common-control register, packets waiting in a router buffer. Its performance is measured by probability of delay, mean waiting time and queue length, rather than by lost-call probability. ```text arrivals +----------+ +-----------+ departures ---lambda-->| queue |---->| N servers |---------> | (buffer) | | (mu each)| +----------+ +-----------+ ``` #### Characteristics in Kendall's notation Kendall's notation describes a simple queue as **A / B / C / K / N / D** (often shortened to A/B/C): | Symbol | Characteristic | Common values | |---|---|---| | A | Arrival process (inter-arrival time distribution) | M = Markovian/Poisson (exponential), D = deterministic, $E_k$ = Erlang-k, G = general | | B | Service (holding) time distribution | M, D, $E_k$, G | | C | Number of parallel servers | 1, 2, ..., N | | K | Capacity of the system (queue + servers) | ∞ by default | | N | Size of the calling population (sources) | ∞ by default | | D | Queue discipline | FIFO/FCFS (default), LIFO, SIRO, priority | 1. **Arrival pattern:** usually Poisson with mean rate $\lambda$ calls per unit time, so inter-arrival times are exponential. 2. **Service pattern:** usually exponential holding time with mean $h = 1/\mu$. 3. **Number of servers** working in parallel. 4. **System capacity:** limited buffers make the system partly a loss system. 5. **Source population:** large (infinite) or small (finite) number of subscribers. 6. **Discipline:** order in which waiting calls are served. **Examples** - **M/M/1:** Poisson arrivals, exponential service, one server — e.g. a single public phone; utilisation $\rho = \lambda/\mu$, mean number waiting $L_q = \rho^2/(1-\rho)$. - **M/M/N** (Erlang C): N trunks with queuing, used for call centres. - **M/M/N/N:** no waiting room — the Erlang B loss system. - **M/D/1:** fixed packet length on a link. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What happens to a call in a queuing (delay) system when all servers are busy? A. It is lost B. It waits in a queue until a server is free C. It is rerouted to a trunk group D. It is held and charged Answer: B. In a delay system calls wait, so performance is measured by delay probability and waiting time rather than loss. (Key point: Queuing system) 2. In Kendall's notation A/B/C, what does C stand for? A. Capacity of the buffer B. Number of parallel servers C. Queue discipline D. Service distribution Answer: B. A = arrivals, B = service distribution, C = number of servers. (Key point: Kendall symbols) 3. What does M in A/B/C mean? A. Deterministic times B. General distribution C. Markovian: Poisson arrivals or exponential service D. Multiple servers Answer: C. M is memoryless: Poisson arrivals / exponential times. (Key point: M meaning) 4. Which system is M/M/N/N? A. Erlang C delay system B. Erlang B loss system with no waiting room C. M/D/1 packet link D. Single server queue Answer: B. Capacity N equals the number of servers, so there is no waiting room: Erlang B. (Key point: M/M/N/N) ## Related in Telecommunications - [Kendall-Lee notation for queuing systems](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Akendall-lee-notation) — Telecommunications, chapter 6, asked 2× - [Short note: Queuing theory in delay system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ashort-note-queuing-delay) — Telecommunications, chapter 6 - [Erlang delay model: notation and derivation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aerlang-delay-kendall-derivation) — Telecommunications, chapter 6 ## Related in other subjects - [Queuing system, characteristics, Kendall notation](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-characteristics-role-kendall) — Simulation and Modeling, chapter 4, asked 2× - [Queuing model, Kendall, M/D/8/15/LIFO](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-model-mdlifo-8) — Simulation and Modeling, chapter 4 - [Queuing characteristics; M/D/6/10/FIFO](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-characteristics-mdfifo-6) — Simulation and Modeling, chapter 4 - [Queuing notation, default values, elements](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-notation-defaults-elements) — Simulation and Modeling, chapter 4