2023/10/02 by Isaac Grosof, Yige Hong, Grosof, Isaac +5 · 2 citations
Business, Management and Accounting · Computer Science · Engineering · #Advanced Queuing Theory Analysis #Cloud Computing and Resource Management #FOS: Computer and information sciences #Performance (cs.PF) #Scheduling and Optimization Algorithms
paper · pdf · doi:10.48550/arxiv.2310.01621
openalex publication_date 2023/10/02 · openalex created_date 2023/10/05 · openalex updated_date 2026/07/28
Multiserver-job (MSJ) systems, where jobs need to run concurrently across many servers, are increasingly common in practice. The default service ordering in many settings is First-Come First-Served (FCFS) service. Virtually all theoretical work on MSJ FCFS models focuses on characterizing the stability region, with almost nothing known about mean response time. We derive the first explicit characterization of mean response time in the MSJ FCFS system. Our formula characterizes mean response time up to an additive constant, which becomes negligible as arrival rate approaches throughput, and allows for general phase-type job durations. We derive our result by utilizing two key techniques: REduction to Saturated for Expected Time (RESET) and MArkovian Relative Completions (MARC). Using our novel RESET technique, we reduce the problem of characterizing mean response time in the MSJ FCFS system to an M/M/1 with Markovian service rate (MMSR). The Markov chain controlling the service rate is based on the saturated system, a simpler closed system which is far more analytically tractable. Unfortunately, the MMSR has no explicit characterization of mean response time. We therefore use our novel MARC technique to give the first explicit characterization of mean response time in the MMSR, again up to constant additive error. We specifically introduce the concept of "relative completions," which is the cornerstone of our MARC technique.