The Multi-Source Probabilistically Preemptive M/PH/1/1 Queue With Packet Errors

Analytical modeling of Age Information (AoI) and Peak AoI (PAoI) has recently drawn a lot attention in the context quantitative assessment information freshness status update systems. In this paper, we study probabilistically preemptive bufferless M/PH/1/1 queue fed with packets from $N$ separate sources for which new packet arrival source- notation="LaTeX">$m$ is allowed to preempt notation="LaTeX">$n$ service, probability depending on . To make model even more general than existing ones, assume distinct phase-type (PH-type) service time distribution, error retransmission probability, each sources. Using sample path arguments theory Markov Fluid Queues (MFQ), exact distributions PAoI are numerically obtained Numerical examples provided demonstrate impact various system parameters performance. two-source system, present methodology how optimally choose preemption probabilities generation rates so as minimize certain AoI-oriented cost functions.