# queueing theory

Queueing theory is a branch of applied mathematics that studies waiting times, throughput, losses, and queue sizes in queueing systems, including buffered packets in routers and switches.

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## Connection pool sizing is a queueing theory problem, not a tuning knob

DevFeed: [Connection pool sizing is a queueing theory problem, not a tuning knob](<https://devfeed.tech/articles/connection-pool-sizing-is-a-queueing-theory-problem-not-a-tuning-knob-39593.md>)

Original publisher: [Read original article](<https://ankit-rana.com/logs/41-connection-pool-sizing-queueing-theory/>)

Author: hello@ankit-rana.com

Published: 2026-08-22T00:00:00Z

Content type: article

Language: en

Sources: [Ankit Rana | Mechanical Sympathy](<https://devfeed.tech/sources/ankit-rana-mechanical-sympathy.md>)

Topics: [connection pool](<https://devfeed.tech/topics/connection-pool.md>), [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>), [Latency](<https://devfeed.tech/topics/latency.md>), [Database](<https://devfeed.tech/topics/database.md>), [Concurrency](<https://devfeed.tech/topics/concurrency.md>)

Tags: [capacity-planning](<https://devfeed.tech/tags/capacity-planning.md>), [concurrency](<https://devfeed.tech/tags/concurrency.md>), [connection-pool](<https://devfeed.tech/tags/connection-pool.md>), [cpu](<https://devfeed.tech/tags/cpu.md>), [database](<https://devfeed.tech/tags/database.md>), [database-performance](<https://devfeed.tech/tags/database-performance.md>), [hikaricp](<https://devfeed.tech/tags/hikaricp.md>), [inference](<https://devfeed.tech/tags/inference.md>), [latency](<https://devfeed.tech/tags/latency.md>), [network](<https://devfeed.tech/tags/network.md>), [postgresql](<https://devfeed.tech/tags/postgresql.md>), [query](<https://devfeed.tech/tags/query.md>), [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>)

### AI overview

This article explains how to size a connection pool using Little's law: concurrency equals throughput multiplied by connection holding time. It argues that increasing the pool beyond the database's parallel execution capacity can move the queue, increase latency, and leave throughput flat. It also identifies excessive holding time from network round trips, N+1 queries, long transactions, and model inference calls as common causes of pool exhaustion.

### Source excerpt

Pool size follows from Little's law: concurrency equals throughput multiplied by holding time, so 500 requests per second each holding a connection for 20ms needs ten connections rather than a round number someone picked. Past the point where the database can execute requests in parallel, adding connections moves the queue rather than removing it, and latency grows while throughput stays flat. The number that actually reaches the database is the pool size multiplied by the instance count, which is usually the number nobody has calculated.

## Managing an Engineer's Week as a Queueing System

DevFeed: [Managing an Engineer's Week as a Queueing System](<https://devfeed.tech/articles/your-week-is-a-queueing-system-and-you-are-running-it-at-100-utilization-39553.md>)

Original publisher: [Read original article](<https://ankit-rana.com/logs/01-time-management-software-engineering/>)

Author: hello@ankit-rana.com

Published: 2026-03-15T00:00:00Z

Content type: opinion

Language: en

Sources: [Ankit Rana | Mechanical Sympathy](<https://devfeed.tech/sources/ankit-rana-mechanical-sympathy.md>)

Topics: [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>), [scheduling](<https://devfeed.tech/topics/scheduling.md>), [systems](<https://devfeed.tech/topics/systems.md>), [Server](<https://devfeed.tech/topics/server.md>)

Tags: [email](<https://devfeed.tech/tags/email.md>), [focus](<https://devfeed.tech/tags/focus.md>), [minutes](<https://devfeed.tech/tags/minutes.md>), [notifications](<https://devfeed.tech/tags/notifications.md>), [productivity](<https://devfeed.tech/tags/productivity.md>), [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>), [scheduling](<https://devfeed.tech/tags/scheduling.md>), [servers](<https://devfeed.tech/tags/servers.md>), [slack](<https://devfeed.tech/tags/slack.md>), [software-engineering](<https://devfeed.tech/tags/software-engineering.md>), [system](<https://devfeed.tech/tags/system.md>), [time-management](<https://devfeed.tech/tags/time-management.md>), [work](<https://devfeed.tech/tags/work.md>)

### AI overview

The article argues that software engineers' schedules behave like queueing systems: near-total utilization increases waiting time, while interruptions evict working context. It recommends maintaining schedule headroom, batching communications, and limiting work in progress.

### Source excerpt

An engineer's week behaves like a queueing system: book yourself at 100% utilization and the wait time for anything new goes vertical, exactly as it does for a server. The fixes are the ones we already use in systems: keep headroom, coalesce interrupts instead of taking them one by one, cap work in progress because Little's law applies to you, and stop letting urgent-but-small tasks hold the lock while important work starves.

## Queueing theory for fun and practice #3: системы с потерями

DevFeed: [Queueing theory for fun and practice #3: системы с потерями](<https://devfeed.tech/articles/queueing-theory-for-fun-and-practice-3-24778.md>)

Original publisher: [Read original article](<https://dev.cheremin.info/2020/08/queueing-theory-for-fun-and-practice-3.html>)

Author: Ruslan Cheremin (noreply@blogger.com)

Published: 2020-08-09T10:59:00Z

Content type: article

Language: ru

Sources: [\>рабочие заметки](<https://devfeed.tech/sources/source-2.md>)

Topics: [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>)

Tags: [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>), [tag-e5017782b67f](<https://devfeed.tech/tags/tag-e5017782b67f.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This article explains queueing systems with losses, where tasks or customers are dropped because of limited buffers, queue capacity, or expiration timeouts. It discusses Erlang-C1 and Erlang-A2 models and their qualitative stability properties.

### Source excerpt

Начальник отдела челобитных Апполинарий Матвеевич любит порядок, поэтому просители могут ожидать его внимания только смиренно сидя в приемной, а не толкаясь возле дверей присутственного места - оттуда их гоняет казак Семен. Какова должна быть посадочная вместимость приемной, чтобы не более 1 просителя в день ушло не солоно хлебавши, если пропускная способность Апполинария Матвеевича не более

## Queueing theory for fun and practice #2: нагрузка и время отклика

DevFeed: [Queueing theory for fun and practice #2: нагрузка и время отклика](<https://devfeed.tech/articles/queueing-theory-for-fun-and-practice-2-24777.md>)

Original publisher: [Read original article](<https://dev.cheremin.info/2020/07/queueing-theory-for-fun-and-practice-2.html>)

Author: Ruslan Cheremin (noreply@blogger.com)

Published: 2020-07-27T15:13:00Z

Content type: tutorial

Language: ru

Sources: [\>рабочие заметки](<https://devfeed.tech/sources/source-2.md>)

Topics: [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>)

Tags: [fifo](<https://devfeed.tech/tags/fifo.md>), [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>), [random](<https://devfeed.tech/tags/random.md>), [tag-e5017782b67f](<https://devfeed.tech/tags/tag-e5017782b67f.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This article explains how system load affects response time through internal queues and buffers. It discusses the characteristic J-curve, the difficulty of deriving a general analytical formula, and how queueing discipline, workload distributions, server allocation, and utilization influence waiting time.

### Source excerpt

Во храме Божьей Матери Поклонской батюшка Иннокентий принимает исповедь у раба божьего обыкновенно минут за 10, а утешения жаждут около 5-и рабов божьих в час. Много ли стульев надобно поставить во храме, дабы исповеди ожидающие не толпились в праздности пред святым алтарем? "Массовое окормление паствы: пособие для начинающих" (редакция 3-я, неизданная) (Часть 2, начало: ТМО, square

## Queueing theory for fun and practice (#1): square root staffing, Little's law

DevFeed: [Queueing theory for fun and practice (#1): square root staffing, Little's law](<https://devfeed.tech/articles/queueing-theory-for-fun-and-practice-1-square-root-staffing-little-s-law-24776.md>)

Original publisher: [Read original article](<https://dev.cheremin.info/2020/07/queueing-theory-for-fun-and-practice-1.html>)

Author: Ruslan Cheremin (noreply@blogger.com)

Published: 2020-07-24T12:35:00Z

Content type: tutorial

Language: ru

Sources: [\>рабочие заметки](<https://devfeed.tech/sources/source-2.md>)

Topics: [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>)

Tags: [operations](<https://devfeed.tech/tags/operations.md>), [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>), [research](<https://devfeed.tech/tags/research.md>), [square](<https://devfeed.tech/tags/square.md>), [tag-88bad1e8f274](<https://devfeed.tech/tags/tag-88bad1e8f274.md>), [tag-e5017782b67f](<https://devfeed.tech/tags/tag-e5017782b67f.md>), [theory](<https://devfeed.tech/tags/theory.md>)

### AI overview

This introductory article begins a series on queueing theory, presenting the author's plan to explain simple, broadly applicable principles, their practical uses, and the assumptions behind them. The planned topics include terminology, capacity and scaling, Little's law, response time versus utilization, and Erlang systems. The author notes that the material is an informal personal summary rather than an expert treatment.

### Source excerpt

На 28-ом этаже центра разработки крупного инвестиционного банка есть 8 туалетных кабинок для людей, идентифицирующих себя с мужским гендером...

## Waiting time paradox #1: автобусы, очереди, и хэш-таблицы

DevFeed: [Waiting time paradox #1: автобусы, очереди, и хэш-таблицы](<https://devfeed.tech/articles/waiting-time-paradox-1-24770.md>)

Original publisher: [Read original article](<https://dev.cheremin.info/2019/04/waiting-time-paradox.html>)

Author: Ruslan Cheremin (noreply@blogger.com)

Published: 2019-04-30T07:37:00Z

Content type: article

Language: ru

Sources: [\>рабочие заметки](<https://devfeed.tech/sources/source-2.md>)

Topics: [queueing theory](<https://devfeed.tech/topics/queueing-theory.md>)

Tags: [queueing-theory](<https://devfeed.tech/tags/queueing-theory.md>), [tag-35a4c7fafefe](<https://devfeed.tech/tags/tag-35a4c7fafefe.md>), [tag-e5017782b67f](<https://devfeed.tech/tags/tag-e5017782b67f.md>), [theory](<https://devfeed.tech/tags/theory.md>), [time](<https://devfeed.tech/tags/time.md>)

### AI overview

The article explains the waiting time paradox using bus arrivals. Although the average interval between buses may be 10 minutes, people are more likely to arrive during longer-than-average intervals, so their average wait can exceed the intuitive estimate of five minutes. It also introduces related examples involving hash-table searches and request processing.

### Source excerpt

Ничего не доводи до крайности: человек, желающий трапезовать слишком поздно, рискует трапезовать на другой день поутру. (Козьма Прутков) ...парадокс времен ожидания, или почему автобуса приходится ждать дольше, чем казалось бы, почему успешный поиск в хэш-таблице скорее всего медленнее, чем неуспешный, и почему иногда среднее время обработки запроса можно уменьшить, если добавить в цикл