Systems with multiple servers under heavy-tailed workloads

Surprising results on task assignment in server farms with high-variability workloads

“…The M/GI/2 with heterogeneous servers has also been looked at by Boxma et al [3], who study how high variability in the job-size distribution at one of the servers affects the other. Finally, while all of the above papers involve analytic solutions, the M/GI/n with high job-size variability has also been studied via simulation by Psounis et al [21]. Here the authors develop an M/GI/n approximation based on two moments of the job size distribution and use that approximation to estimate the optimal number of servers.…”

How many servers are best in a dual-priority system?

“…The fundamental question of "how many servers are best" has been asked by a stream of research [20,30,17,27,26,28] discussed in Section 2.2. All of this work considers the system where jobs are serviced in first-come-first-served (FCFS) order, and asks both whether a single fast server is preferable to k slow servers (of equal total capacity) and how the optimal number of servers varies across workloads.…”

Single server queueing model with Gumbel distribution using Bayesian approach

“…The Markov chain has converged in both informative and non-informative priors since it likely to be sampling from the stationary distribution and horizontal band, with no long upward or downward trends as shown in Figure [15, 16, 17, 18]. Moreover, the autocorrelation is almost negligible for all the model parameters (see Figure[19 [23,24,25,26]) for checking the convergence of the algorithm. Also, the Monte Carlo Error (MC.E) of Gumbel/Gumbel/1 queueing model is presented Table.1 & Table.3.…”

“…In this regard, serveral authors have been devoted by queueing models based on the heavy tailed distribution [13], [15], [26]. Weibull, Parato, log-normal, Burr type III, Burr type XII and Gumbel distributions are some heavy tailed behaviour distributions [19].…”