On the analytical model for jitter

Jitter in Internet Protocol (IP) networks refers to the variation in packet arrival times, which can cause delays or disruptions in real-time communications like voice or video calls. Managing jitter is crucial for applications requiring consistent data flow, such as voice over internet protocol, online gaming, and video conferencing, to maintain quality and reliability. Dahmouni et al. derived an analytical model for jitter in an important paper cited by many authors. But some of the fundamental equations in Dahmouni et al. do not appear correct. We correct the equations and study some analytical properties of jitter. Among others, we show that jitter can be expressed as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>η</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>η</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:mfenced><mml:mi>μ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>η</mml:mi><mml:mo>+</mml:mo><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mrow></mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math> denotes the rate of service times, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mi>η</mml:mi></mml:mrow></mml:math> denotes the rate of transit times and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math> denotes the rate of inter-arrival times. We provide a Maple code to check correctness of our equations.