# A Study Comparing Waiting Times in Global and Local Queuing Systems with Heterogeneous Workers
## 5 Discussion and Concluding Remarks  
Our simulation results show that GH performs slightly better than LH, but the results are controversial for GHT and LHT. We demonstrate that push mechanisms that manage the assignment procedures and heterogeneity-aware algorithms enhance the waiting time in local queue systems and balance the workload, especially when multiple processing rate categories classify the workers. We compared different architectures and routing policies for groups of 3 to 12 workers categorized by their processing rates and for two load levels: regular (0.8) and high (0.93). Setting the number of processing rates to three categories is important since it reflects the real-world case, and previous work is usually used to simulate only two categories. We discovered that JSQ's fastest TB routing policy for local queues is more effective when assigning tasks to medium and fast workers than global queues. In a local queue environment, the control mechanism makes the assignment of slow workers easier to fix. Our research suggests that WJSQL can reduce the system's average waiting times, particularly the tasks assigned to the slow workers. For all heterogeneity-aware policies, it is crucial to use the actual processing rates of workers by monitoring and applying online learning of the processing rate. The JSQ Fastest TB is simple to implement, knowing the rates. Given the same load, the simulation results show that all the systems demonstrated decreased waiting times when the number of workers increased. This statistical fact was discussed in the literature but not in the context of global and local queues. We expected the waiting time to remain the same because the number of servers was scaled up with the arrival rate, so the average server utilization stayed the same. In this study, the larger number of workers was 12, but we have already seen that the decrease tends to converge, especially when the load is 0.93. The following research on this subject should include more workers in a real marketplace and find the link between the decrease in wait time and the JSQ policies. Local queue architecture is a common feature of many systems that use digital servers or human workers as part of their workforce. Applying appropriate routing policies to optimize performance and resource utilization is essential. In environments with fluctuating workloads, exploring various routing strategies is crucial. For example, call centers may need to adapt scheduling based on agents' availability and skills, especially during peak times like lunch hours or evenings. In cloud computing, strategies may focus on the dynamic allocation of computational resources to manage demand spikes efficiently. These variable workloads require adaptive algorithms that adjust scheduling policies based on real-time conditions, highlighting the importance of robust system design to accommodate diverse and dynamic workload scenarios. Our study examined the WJSQL routing strategy and learned workers' processing rates. We plan to conduct further studies to analyze the sensitivity of the WJSQL strategy to process rate changes, enhancing our understanding of its adaptability. Today, organizations that provide services that use local queues implement local queue infrastructure. For example, a virtual marketplace management system. Message queue (MQ) systems, such as Apache Kafka or RabbitMQ, implement an asynchronous communication pattern between applications operated over different computer systems. The system paradigm follows the publish/subscribe model, where messages are placed in the queue until the recipient pulls them. MQ systems do not provide a service for a local queueing system. After highlighting the advantages and importance of heterogeneity-aware routine policies, we plan to add push control and dedicated architecture into message queues. This will make them suitable for systems with human workers and others. Conceptualization, I.A. and M.A. ; methodology, I.A. ; software, E.T. ; validation, E.T. ; formal analysis, I.A. and M.A.