FUTURE RESEARCH
In this chapter, we briefly discuss some possible extensions to our study for future research. We first propose some possibilities for dynamic control problems.
Multiple servers: Consider the parallel-series queueing network which is described in Chapter 3, as shown in Figure 3.1. In our work, we consider a single flexible server to be able to work at any of the service stations. To extend this, we may consider allocating multiple servers. Suppose that each server is allowed to work at any of the K service stations. Service times at a service station follow a given distribution which depends only on the service station. We may consider collaborative or non-collaborative servers.
Emergency v.s. non-emergency: Consider a system with an emergency station and non-emergency stations. For example, in a hospital system, the emergency room is usually given the top priority over other clinical units. We may model this system by a parallel system as shown in Figure 3.3. Suppose that station 1 is an emergency station which has absolute priority over other non-emergency stations (preemptive priority). A single flexible server is assigned to work at the emergency and non-emergency stations. Future work could investigate how to prioritize non-emergency stations to maximize the long-run average throughput of the system.
Collaborative station: Consider a system with stations which require more than one servers to process a request. We may use the parallel system with two service stations as shown in Figure ??to model it. Suppose there are two flexible servers working at station 1 and 2. The service operation at station 1 requires two servers, while the service operation at station 2 needs only one server. Service times are random variables whose distributions depend only on the service station. Suppose preemption is not allowed. Future work could seek the optimal policy to maximize the long-run average throughput of the system.
Next, we provide some possible extensions to our static design problems.
Multiple servers: Consider the closed queueing network studied in Chapter 4. In our work, we consider allocating a fixed amount of continuous service resource to theK service stations. Another consideration can be allocating discrete service resource, i.e., multiple servers. Suppose that each server is able to work at any of the K service stations. Service times at a service station follow a given distribution which depends only on the service station. We may consider either collaborative or non-collaborative servers.
Waiting cost minimization: In our work, we consider maximizing the long-run average throughput of the system. We may consider waiting cost setup for the design problems. Suppose cost is incurred when customers are waiting in the service stations at the second stage, either waiting in the queue or being served. The cost rate depends only on the service stations. Assume that a fixed amount of service resource is available to be allocated to each of the K service stations. We are interested in looking for optimal allocation in order to minimize the long-run average total waiting cost of the system. We expect that the optimal allocation would assign more service resource to a service station which has a higher cost rate.
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