Queueing Models in Computer Networks 

 Queueing Model Kya Hota Hai?

Jab network par bahut saare data packets ek server ya router par aate hain, to wo line (queue) mein lag jaate hain. Queueing model help karta hai yeh samajhne mein ki:

• Packets kitni speed se aa rahe hain (arrival rate)

• Ek packet ko process karne mein kitna time lagta hai (service rate)

• System mein kitna delay ho raha hai

• Kitne servers available hain

• Kya packet drop hote hain agar jagah nahi hai?

Socho ek ATM par log line mein lag rahe hain — yeh ek queue hai. Har aadmi ek packet ki tarah hai jo wait kar raha hai server (ATM machine) se serve hone ke liye.

 Important Terms:

 Little’s Theorem – Super Simple Formula

Formula: L = λ × W

 Example:

• 5 packets/sec aa rahe hain (λ = 5)

• Har packet 0.4 sec rukta hai (W = 0.4)

• To system mein average 5 × 0.4 = 2 packets hamesha hote hain

 Common Queueing Models (Kendall’s Notation)

Queueing models ko likhne ka ek format hota hai:
A/S/c

• A (Arrival) → kaise packets aate hain (M = exponential)

• S (Service) → server kaise process karta hai (M ya G)

• c (Servers) → kitne servers hain

M = “Memoryless” yaani exponential distribution (most common),
G = General (koi bhi distribution)

 M/M/1 Queue – Sabse Basic Aur Common Model

 Diagram:

 Use Case:

• Ek router ya printer jahan sabko line mein wait karna padta hai

 Example:

• λ = 4/sec, μ = 5/sec

• ρ = λ / μ = 4 / 5 = 0.8 → server 80% time busy hai

• Delay = 1 / (μ – λ) = 1 second average waiting time

Agar ρ 1 se zyada ho gaya, to queue kabhi khatam nahi hogi!

 M/M/m Queue – Jab Ek Se Zyada Server Hain

 Diagram:

 Use Case:

• Call centers (multiple agents)

• Zomato kitchen jahan ek se zyada chef ho

 Example:

• λ = 12/sec, μ = 4/sec, m = 4 servers

• Total capacity = 4 × 4 = 16/sec

• Utilization = 12 / 16 = 0.75 → servers 75% time busy

 M/M/∞ Queue – Unlimited Servers, No Waiting

 Diagram:

 Use Case:

• Cloud-based apps jaise Google Search, ChatGPT etc.

• Har user ko instantly ek server mil jaata hai

 Feature:

• Koi queue nahi hoti, har request instantly serve hoti hai

 M/M/m/m Queue – Fixed Servers, No Queue, Request Drop

 Diagram:

 Use Case:

• Mobile networks jahan limited calling channels hote hain

• Agar 4 calls chal rahi hain aur 5th aayi → busy tone

Isse Blocking Probability calculate karne ke liye Erlang B formula use hota hai

 M/G/1 Queue – Flexible Service Time, 1 Server

 Use Case:

• Web server jahan kabhi chhoti file (image) aur kabhi badi file (video) serve hoti hai

• Service time fix nahi hota

 Note:

• Ye zyada realistic model hai, but complex calculations hoti hain

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 Full Comparison Table 

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 Summary 

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 Real Life Analogy Summary