# A Study Comparing Waiting Times in Global and Local Queuing Systems with Heterogeneous Workers
## 2 Related Work
### Global vs. Local Queues Comparison  
Global queue architecture is a way to reduce the average waiting time without increasing staffing levels. This is achieved through pooling benefits. [PERSON] et al. [25] present a system with a collection of local task queues and a simple distributed load-balancing scheme well-suited for scheduling tasks in shared memory parallel machines. Typically, task scheduling on such machines has been performed through a single, globally accessible work pile. However, the scheme introduced in this paper achieves balanced utilization comparable to that of a global work-pile. [PERSON] & [PERSON] [26] analyzed local queue architecture with JSQ with different load balancing rules in a contemporary scaling regime when workers were homogenous. They compared it with the global queue architecture and found that dispatching jobs to servers instead of storing them in a global queue costs 15%. The homogenous case is relatively easy since all the workers have the same mean rate, and the higher number of tie-breaking cases causes the price of dispatching jobs to the local queue. Thus, it does not reflect the real world since workers' service rates in most systems are not homogenous. [PERSON] & [PERSON] [21], who proposed a SA-JSQ scheme for both local queue settings and the global queue setting in scenarios where the system size is infinite, also obtained a lower bound on the mean response time for local and global queues and showed that this lower bound is better when the system uses global queue architecture. They did not express the mean response time of a task assigned to a specific category since they only discussed the lower bound.  
The research studies described so far deal with systems where workers are digital processors or servers rather than human workers. The latest research shows that a system with human strategic workers performs better regarding workers' processing rates in a system with parallel queues rather than in a global queue system. These studies are about the change in workers' processing time rather than heterogeneous workers, but still, it is important to compare global and local queues. [PERSON] et al. [27] studied how queue design affects human worker productivity in service systems. The study found that a single-queue architecture or poor visibility of the queue length in local queues slows down servers. [PERSON] et al. [28] developed a general framework to analyze the influence of system load (queue length) on workers' service times. [PERSON] et al. [5] developed analytical models that incorporate human behavior for both types of queuing. They evaluated system performance based on the expected waiting time and total time. They established threshold values to identify situations where parallel systems outperform single queue systems for different workloads, system sizes, and speedup and slowdown effects. [PERSON] et al. [29] & [PERSON] et al. [30] studied the question of whether to operate a dedicated (local) system or a pooled (global) system by analyzing a model in which delay-sensitive customers could access their delay information (e.g., by observing the queue length or receiving real-time expected delay information) and make their joining or leaving decisions based on that information. They proved that pooling (global) queues can result in much worse performance than a dedicated system, even with identical servers and homogeneous customers.  
To summarize, all the studies presented show that the superiority of a global queue system when workers are heterogeneous is not apparent. There are a lot of system and workload parameters, as well as behavioral terms, which show otherwise.