M/M/1/K Queue Validation

An OMNeT++ simulation of a finite-buffer M/M/1/K queue, validated against closed-form analytical results.

Model

Source --> Queue --> Sink

• Source: Poisson arrivals (exponential inter-arrival times)
• Queue: Exponential service, finite capacity K (including job in service), drops when full
• Sink: Absorbs completed jobs, records sojourn time

Parameters

Parameter	Value
λ (arrival rate)	0.8
μ (service rate)	1.0
K (system capacity)	5
Simulation time	100 000 s
Repetitions	5

Analytical Reference (M/M/1/K)

With ρ = λ/μ = 0.8:

Metric	Formula	Value
P(drop)	π_K = π_0 · ρ^K	0.088819
Throughput	λ · (1 − P_drop)	0.728944
Utilization	1 − π_0	0.728944
E[N]	Σ n·π_n	1.868332
E[T]	E[N] / throughput	2.563065

Building and Running (via opp_repl)

from opp_repl import *

load_opp_file("/home/levy/workspace/mm1k/mm1k.opp")
p = get_simulation_project("mm1k")
build_project(simulation_project=p)
r = run_simulations(simulation_project=p, config_filter="Mm1kValidation")

Files

File	Description
mm1k.opp	opp_repl project descriptor
Network.ned	Network topology and module declarations
Source.h / Source.cc	Poisson arrival generator
Queue.h / Queue.cc	Finite-capacity queue with exponential service
Sink.h / Sink.cc	Job sink, records lifetime statistics
omnetpp.ini	Simulation configuration

Recorded Statistics

• generated — total jobs created (Source)
• accepted / dropped / dropProbability — queue admission (Queue)
• busy:timeavg — server utilization (Queue)
• queueLength:timeavg — mean number in system (Queue)
• lifeTime:mean — mean sojourn time (Sink)

Validation Results

Metric	Analytical	Simulated	Rel. Error
Drop probability	0.088819	0.089923	1.24%
Throughput	0.728944	0.727422	0.21%
Utilization	0.728944	0.727225	0.24%
E[N]	1.868332	1.864657	0.20%
E[T]	2.563065	2.563365	0.01%

All errors are below 1.3%, consistent with statistical noise.