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High Speed Droplet-based Delivery System for Passive Pumping in Microfluidic Devices

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On the Transient Queue with the Dropping Function.

Andrzej Chydzinski¹

¹Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

This study analyzes a queueing system where packet loss probability depends on queue size, crucial for Internet router active queue management. Results show transient queue behavior varies with dropping functions, even when steady-state performance is unchanged.

Keywords:

Internet routers M/G/1 active queue management dropping function queueing model transient analysis

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Area of Science:

Computer Science
Applied Mathematics
Network Engineering

Background:

Active queue management (AQM) schemes are vital for Internet router performance.
Packet dropping based on queue size is a common AQM strategy.
Understanding transient behavior is critical for AQM effectiveness.

Purpose of the Study:

Analyze transient characteristics of a queueing system with size-dependent packet dropping.
Determine the probability of maintaining queue size below a specific level over time.
Calculate the average time to reach a predefined queue size level.

Main Methods:

Derivation of theoretical results for transient queue characteristics.
Analysis of a queueing model with size-dependent packet dropping probability.
Numerical examples to illustrate theoretical findings.

Main Results:

The probability of keeping queue size under a predefined level is derived.
The average time to reach a given queue size level is calculated.
Transient queue behavior is shown to be sensitive to the dropping function's shape.

Conclusions:

The analyzed queueing scheme's transient behavior is significantly influenced by the dropping function.
Different dropping functions can lead to distinct transient dynamics, even with identical steady-state performance.
This highlights the importance of considering transient analysis in AQM design.