# A Study Comparing Waiting Times in Global and Local Queuing Systems with Heterogeneous Workers
A system with parallel and local queues can be more effective, as it motivates human workers to complete their tasks locally, resulting in better performance regarding workers' processing rates. This, in turn, leads to shorter queue lengths [5]. Local queue systems provide an opportunity to tailor task routing to individual worker capabilities, promising load-balancing improvements and reduced waiting times. We use the abbreviations GH, GHT, LH, and LHT to refer to the four systems we investigate in our study. The first letters (G or L) refer to the queueing architecture, with G for global and L for local. The other letter (H or HT) refers to server types, with H for homogenous and HT for heterogeneous. Choosing between global and local queue architectures is not straightforward. Most of the studies assumed that all workers have similar processing rates. Analyzing a system with servers with processing rates can be challenging due to the large number of parameters involved (system load, workload distribution, arrival rate, number of workers, processing rates, and categories). Queuing architecture adds various configurations, such as queue management (FIFO or round-robin), dispatch policies (shortest or weighted queue), and routine policies. Papers that have analyzed waiting times in settings with heterogeneous workers have used different settings, such as considering a small number of workers or infinite system sizes and assuming low or high system loads. The comparative effectiveness of these systems in environments with varied worker speeds remains the subject of ongoing research. Almost no papers compare the performance of local vs. global queues in a setting where the workers are heterogeneous. In this paper, we address this gap in the literature and use discrete event simulation (DES) to compare the two architectures in a system with homogenous Poisson arrivals and exponentially distributed service times. We compare the GHT and LHT systems in terms of their performance measured by waiting time and load distribution among the workers. We also compare the performance of the GHT and GH systems and of the LH and LHT systems. It is statistically acceptable to prioritize waiting times over response times when workers' task arrival and processing rates follow the Poisson distribution (M/M/K); the system load is above 0.5. This has been demonstrated in real-world marketplace data gathered through crowdsourcing by [PERSON] et al. [3]. The main contributions of this work are listed below. 1. A literature review, including the following: * Identifying and describing papers that compare GH and GHT systems (Section 2.1). We found that most of the studies considered only systems with few servers. * Identifying and discussing papers dedicated to the LH and LHT systems (Section 2.2). Most of these papers assume very large-to-infinite system sizes and show that the JSQ routing policy effectively keeps waiting times low for the LH system. We found no papers directly comparing the waiting time performance of LH and LHT systems. * Identifying heterogeneity-aware routing policies discussed in the LHT literature. Our simulation studies the comparative performance of the Shortest Expected Delay (SED) and the speed-aware routing. * Reviewing the literature on handling tie-breaking (TB) events in local queueing architectures. A tie-breaking event occurs when several servers meet the same condition for task routing (for example, the same value for expected delay), and the scheduler needs to select one of the servers. With random TB routing, the server is chosen at random. The literature discusses other tie-breaking algorithms such as fastest TB, local JSQ random TB, and local JSQ fastest TB routing policies for homogeneous and heterogeneous settings. The local weighted JSQ with learning (WJSQL) is our version of SED. Identifying and discussing a limited number of papers comparing GH and LH systems and recognizing that there are even fewer papers comparing GHT and LHT systems (Section 2.3). 2.