On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study

Abstract

We consider the multi-server, single-channel queue, i.e., a G / G / k queue with k identical servers in parallel, under the first-come-first-served discipline in which the inter-arrival process is non-Poisson, the service time has any given distribution, and traffic is of medium intensity. Such queues are common in factories, airports, and hospitals, where the inter-arrival times and service times are typically not exponentially distributed, but rather have double-tapering distributions whose probability density functions taper on both sides, e.g., gamma, triangular etc. For these conditions, a new closed-form approximation based on only the mean and variance of the two inputs, the inter-arrival and service times, is presented. Determining distributions of inputs typically requires additional human effort in terms of histogram-fitting and running a goodness-of-fit test, which is avoided here. The new approximation is tested on a variety of scenarios and its performance is benchmarked against simulation. Further, the new approximation is also implemented on a ventilator case study from the recent COVID-19 pandemic to demonstrate its utility in optimizing server capacity. The approximation provides errors typically in the range 1–15% and 31% in the worst case. In systems where data change rapidly and decisions must be made quickly, this approximation will be particularly useful.

Modelling Dynamic Traffic Loads in Multiserver Queues using G/G/k Queue

“…In [2], the author discusses discrete time Geo/G/1 queue in which the server operates a random threshold policy mainly (p, N)-policy. Using generating function techniques, the system state evaluation is analyzed and the long run average cost function per unit time is developed to determine the optimal values of p and N. Chaves et.al [3], provides a new closed-form approximation for a multiserver, single-channel queue with k identical servers in parallel, using only the mean and variance of the inter-arrival and service periods. The method avoids histogram-fitting and goodness-of-fit tests for input distributions.…”

Scaling A Blockchain-Based System Via Optimized Load Balancing Among Shards

“…We have proposed a novel approach that leverages the M/M/k model, Poisson distribution, and Exponential distribution to optimize load balancing in Blockchain systems. The M/M/k model, a well-known method in queueing theory, is used to distribute nodes within shards, ensuring an even allocation of computational resources [18] [19]. The Poisson distribution is employed to model the arrival of incoming queries, reflecting the random nature of transaction requests in a Blockchain network [20].…”