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Queuing system, characteristics, Kendall notation
Short answer
A queuing system involves customers, a queue, and servers. Characteristics include arrival/service distributions, number of servers, queue discipline, and capacity. In simulation, queuing models provide waiting times and utilization for complex systems; analytical formulas like M/M/1 aid validation. Kendall notation A/B/c/K/N/D: M/M/1 denotes Poisson arrivals, exponential service, one server.
What is a queuing system? List the various characteristics of a queuing system. Explain the role of queuing system in simulation study. Explain Kendall notation with example.
Queuing system
A queuing system consists of customers (arrivals) who come to a service facility, wait in a queue if the server is busy, are served, and then leave. Examples: bank counter, hospital OPD, CPU job queue, traffic at a signal.
Characteristics of a queuing system
- Calling population: the source of customers; finite or infinite.
- Arrival process: how customers arrive (usually Poisson, so exponential inter-arrival times), singly or in batches.
- Service mechanism: distribution of service times and number of servers (single or multiple, parallel or in series).
- Queue discipline: the rule for choosing the next customer: FCFS, LIFO, priority, random.
- System capacity: maximum number allowed in the queue (finite or infinite).
- Customer behaviour: balking (not joining), reneging (leaving after waiting), jockeying (changing queues).
- Number of service stages: single stage or several in series.
Role in simulation study
- Many systems studied by simulation (banks, computer networks, CPUs, factories, traffic) are queuing systems, so queue models are the building blocks of discrete-event simulation.
- Simulation provides performance measures such as average waiting time, queue length, server utilization and probability of delay, when the distributions are too complex for formulas.
- Analytical formulas (M/M/1, M/M/c) give a quick estimate to verify and validate the simulation model.
- It allows what-if studies, e.g. effect of adding a server, without disturbing the real system.
Kendall notation
A queue is described by A/B/c/K/N/D:
| Symbol | Meaning |
|---|---|
| A | Inter-arrival time distribution |
| B | Service time distribution |
| c | Number of parallel servers |
| K | System capacity (default infinity) |
| N | Size of calling population (default infinity) |
| D | Queue discipline (default FCFS) |
Distribution codes: M = Markovian (Poisson arrivals or exponential times), D = deterministic (constant), E_k = Erlang with k phases, G = general (any distribution).
Example 1: M/M/1 is Poisson arrivals, exponential service, one server, infinite capacity and population, FCFS. With arrival rate 4/hour and service rate 6/hour: utilization 0.667, average number in system 2, average time in system 0.5 hour.
Example 2: M/D/3/50 is Poisson arrivals, constant service time, 3 servers, at most 50 customers in the system, infinite population, FCFS.
✓ Answer checked by Claude Opus 5.5 (high effort)
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