2019/05/31 by Alkan Soysal, Şennur Ulukuş, Soysal, Alkan +1 · 7 citations
Computer Science · Social Sciences · #Age of Information Optimization #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Networking and Internet Architecture (cs.NI) #Retirement, Disability, and Employment #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1905.13743
openalex publication_date 2019/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the age of information in G/G/1/1 systems under two service\ndiscipline models. In the first model, if a new update arrives when the service\nis busy, it is blocked; in the second model, a new update preempts the current\nupdate in service. For the blocking model, we first derive an exact age\nexpression, then we propose two simple to calculate upper bounds for the\naverage age. The first upper bound assumes the interarrival times to have\nlog-concave distribution. The second upper bound assumes both the interarrivals\nand service times to have log-concave distribution. Both upper bounds are tight\nin the case of M/M/1/1 systems. We show that deterministic interarrivals and\nservice times are optimum for the blocking service model. In addition, using\nthe age expression for G/G/1/1 systems, we calculate average age expressions\nfor special cases, i.e., M/G/1/1 and G/M/1/1 systems. Next, for the preemption\nin service model, we first derive an exact average age expression for G/G/1/1\nsystems. Then, we propose a simple to calculate upper bound for the average\nage. In addition, similar to blocking discipline, using the age expression for\nG/G/1/1 systems, we calculate average age expressions for special cases, i.e.,\nM/G/1/1 and G/M/1/1 systems. Average age for G/M/1/1 can be written as a\nsummation of two terms, the first of which depends only on the first and second\nmoments of interarrival times and the second of which depends only on the\nservice rate. In other words, interarrival and service times are decoupled. We\nshow that deterministic interarrivals are optimum for G/M/1/1 systems. On the\nother hand, we observe for non-exponential service times that the optimal\ndistribution of interarrival times depends on the relative values of the mean\ninterarrival time and the mean service time.\n