Real-Time Status Update System in a Parallel Blocking Queue

Multi-path transmission is promising in improving the freshness of information received in status-updating systems. However, multi-path transmission results in out-of-order arrivals at the monitoring point, which poses significant challenges to the analysis of freshness. This work analyzes the age of information (AoI) of a multi-path transmission non-preemptive system where multiple servers can deliver the information generated from a source to a common monitor. Two systems are considered: the homogeneous M/M/n/n non-preemptive system, where the arrival rates and service rates are identical across servers, and the heterogeneous M/M/2/2 non-preemptive system, where the service rates of all servers are different. We employ the stochastic hybrid systems (SHS) approach to characterize the average AoI of the systems and derive an explicit expression for the average AoI in both homogeneous and heterogeneous cases. Numerical results verify the effectiveness of the analysis. It is shown that when the number of servers increases in powers of 2, the most significant reduction in the average AoI occurs when the number of servers changes from 1 to 2. Besides, the numerical results confirm that the M/M/2/2 non-preemptive system is superior to the M/M/1/1 dual-queue system in terms of average AoI.