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Queuing characteristics; D/M/1/LIFO/20/510

Short answer

Characteristics: calling population, arrival pattern, service mechanism, number of servers, queue discipline, capacity, customer behaviour. D/M/1/LIFO/20/510: deterministic inter-arrivals, exponential service, 1 server, last-in first-out discipline, capacity 20, finite population 510. Applications: banks, CPU scheduling, call centres, traffic control, manufacturing.

What are the characteristics of a queuing system? What is the meaning of D/M/1/LIFO/20/510 in queuing system? Write down the application of queue.

Characteristics of a queuing system

A queuing system has customers who arrive, wait if needed, get service and depart. Its main characteristics are:

  1. Calling population: finite or infinite source of customers.
  2. Arrival pattern: distribution of inter-arrival times (Poisson, constant, general), single or batch arrivals.
  3. Customer behaviour: balking, reneging and jockeying.
  4. Service pattern: service time distribution (exponential, constant, general).
  5. Number of servers: single or multiple; parallel or in series.
  6. Queue discipline: FIFO, LIFO, SIRO, priority.
  7. System capacity: maximum number in the system, infinite or finite.
  8. Queue layout: one shared queue or one queue per server.

Meaning of D/M/1/LIFO/20/510

The standard Kendall order is arrival / service / servers / capacity / population / discipline (A/B/c/K/N/Z). Here the discipline is written in the fourth place, so the code is read as:

FieldMeaning
DDeterministic arrivals: customers arrive at fixed, equal intervals
MMarkovian service: exponentially distributed service times
1A single server
LIFOLast in, first out: the newest waiting customer is served first
20Maximum of 20 customers in the system at a time (if read as capacity)
510Calling population of 510 customers (finite source)

Example: a machine feeds items into a stack at regular intervals; a single worker picks the top (latest) item, taking a random time. The stack holds at most 20 items, and the items come from 510 possible units. (Some books place the last two numbers in the order population / capacity; the idea is the same: one is the capacity and the other is the population.)

Applications of queues

  • Banks, ticket counters and supermarket checkouts.
  • Computer systems: CPU scheduling, disk requests, print spooling and network packet buffers.
  • Telephone exchanges and call centres.
  • Hospitals (OPD, emergency), traffic signals and toll plazas.
  • Manufacturing: jobs waiting for machines on an assembly line.

✓ Answer checked by Claude Opus 5.5 (high effort)

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