Everything about M/M/c queue

🧭 Start here: a 6-step reading path

1. Read the overview: M/M/c queueA 5-minute orientation
2. Skim a recent paper: Queue length estimation for signal controlling in a connected environmentInfluential work since 2022
3. Pick up a classic book: Java software solutionsThe most-reprinted book on the subject
4. Read the landmark paper: The Regulation of Queue Size by Levying TollsCited 1,088 times
5. Go sideways: M/D/1 queueA closely related topic
6. Go sideways: Pollaczek–Khinchine formulaA closely related topic

🏆 Landmark papers (most cited)

• The Regulation of Queue Size by Levying Tolls

  P. Naor · 1969 · Econometrica · 1,088 citations

• The stability of a queue with non-independent inter-arrival and service times

  R. M. Loynes · 1962 · Mathematical Proceedings of the Cambridge Philosophical Society · 879 citations

• New results on the single server queue with a batch markovian arrival process

  David M. Lucantoni · 1991 · Communications in Statistics. Stochastic Models · 867 citations

• REM: active queue management

  S. Athuraliya, S.H. Low, V.H. Li · 2001 · IEEE Network · 734 citations

• Stability, queue length, and delay of deterministic and stochastic queueing networks

  Cheng-Shang Chang · 1994 · IEEE Transactions on Automatic Control · 695 citations

• Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations

  S. W. Fuhrmann, Robert B. Cooper · 1985 · Operations Research · 513 citations

• Optimal Incentive-Compatible Priority Pricing for the M/M/1 Queue

  Haim Mendelson, Seungjin Whang · 1990 · Operations Research · 461 citations

• A duality model of TCP and queue management algorithms

  S.H. Low · 2003 · IEEE/ACM Transactions on Networking · 453 citations

🆕 Influential since 2022

• Queue length estimation for signal controlling in a connected environment

  Ahmad Abutahoun, Taqwa Alhadidi, Nidhal Saada · 2025 · Expert Systems with Applications · 104 citations

• DRL-Based Computation Offloading With Queue Stability for Vehicular-Cloud-Assisted Mobile Edge Computing Systems

  Guifu Ma, Xiaowei Wang, Manjiang Hu · 2023 · IEEE Transactions on Intelligent Vehicles · 80 citations

• Estimating key traffic state parameters through parsimonious spatial queue models

  Qixiu Cheng, Zhiyuan Liu, Jifu Guo · 2022 · Transportation Research Part C: Emerging Technologies · 77 citations

• IRS Assisted NOMA Aided Mobile Edge Computing With Queue Stability: Heterogeneous Multi-Agent Reinforcement Learning

  Jiadong Yu, Yang Li, Xiaolan Liu · 2023 · IEEE Transactions on Wireless Communications · 73 citations

• Research on eco-driving optimization of hybrid electric vehicle queue considering the driving style

  Shaohua Wang, Pengfei Yu, Dehua Shi · 2022 · Journal of Cleaner Production · 71 citations

📚 Books worth reading

• Java software solutionsLewis, John, John E. Lewis Ph. D. · 1997
• C How to ProgramPaul J. Deitel, Harvey M. Deitel · 2007
• AlizéFrance Robitaille, Marjorie Perreault · 2003
• Contes des féesCharles Perrault · 1862
• Data Communications and NetworkingBehrouz A. Forouzan, Catherine Ann Coombs · 2000
• An introduction to computer scienceJean-Paul Tremblay, Richard B. Bunt · 1979
• Data structures and algorithm analysis in CMark Allen Weiss · 1993
• Starting Out with JavaTony Gaddis · 2004

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• M/D/1 queue In queueing theory, a discipline within the mathematical theory of probability, an M/D/1 queue represents the queue length in a system having a single…
• Pollaczek–Khinchine formula In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue…
• M/M/1 queue In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single…
• Birth–death process The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types:…
• M/M/∞ queue In queueing theory, a discipline within the mathematical theory of probability, the M/M/∞ queue is a multi-server queueing model where every arrival experiences…
• Jackson network In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes called a Jacksonian network) is a class of…
• M/G/1 queue In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated…
• Knudsen number The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale…