In a ride-sharing system, arriving customers must be matched with available drivers. These decisions affect the overall number of customers matched, because they impact whether future available drivers will be close to the locations of arriving customers. A common policy used in practice is the closest driver policy, which offers an arriving customer the closest driver. This is an attractive policy because it is simple and easy to implement. However, we expect that parameter-based policies can achieve better performance. We propose matching policies based on a continuous linear program (CLP) that accounts for (i) the differing arrival rates of customers and drivers in different areas of the city, (ii) how long customers are willing to wait for driver pickup, (iii) how long drivers are willing to wait for a customer, and (iv) the time-varying nature of all the aforementioned parameters. We prove asymptotic optimality of a forward-looking CLP-based policy in a large market regime and of a myopic linear program-based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates and parameters are time homogeneous, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers under mild conditions.
In a ride-sharing system, arriving customers must be matched with available drivers. These decisions affect the overall number of customers matched, because they impact whether future available drivers will be close to the locations of arriving customers. A common policy used in practice is the closest driver policy, which offers an arriving customer the closest driver. This is an attractive policy because it is simple and easy to implement. However, we expect that parameter-based policies can achieve better performance. We propose matching policies based on a continuous linear program (CLP) that accounts for (i) the differing arrival rates of customers and drivers in different areas of the city, (ii) how long customers are willing to wait for driver pickup, (iii) how long drivers are willing to wait for a customer, and (iv) the time-varying nature of all the aforementioned parameters. We prove asymptotic optimality of a forward-looking CLP-based policy in a large market regime and of a myopic linear program–based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates and parameters are time homogeneous, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers under mild conditions.
We consider the problem of controlling a two-server Markovian queueing system with heterogeneous servers. The servers are differentiated by their service rates and reliability attributes (i.e., the slower server is perfectly reliable, whereas the faster server is subject to random failures). The aim is to dynamically route customers at arrival, service completion, server failure, and server repair epochs to minimize the long-run average number of customers in the system. Using a Markov decision process model, we prove that it is always optimal to route customers to the faster server when it is available, irrespective of its failure and repair rates, if the system is stable. For the slower server, there exists an optimal threshold policy that depends on the queue length and the state of the faster server. Additionally, we analyze a variant of the main model in which there are multiple unreliable servers with identical service rates, but distinct reliability characteristics. For that case it is always optimal to route customers to idle servers, and the optimal policy is insensitive to the servers’ reliability characteristics.
Networks in which the processing of jobs occurs both sequentially and in parallel are prevalent in many application domains, such as computer systems, healthcare, manufacturing, and project management. The parallel processing of jobs gives rise to synchronization constraints that can be a main reason for job delay. In comparison with feed-forward queueing networks that have only sequential processing of jobs, the approximation and control of networks that have synchronization constraints is less understood. One well-known modeling framework in which synchronization constraints are prominent is the fork-join processing network. Our objective is to find scheduling rules for fork-join processing networks with multiple job types in which there is first a fork operation, then activities that can be performed in parallel, and then a join operation. The difficulty is that some of the activities that can be performed in parallel require a shared resource. We solve the scheduling problem for that shared server (that is, which type of job to prioritize at any given time) when that server is in heavy traffic and prove an asymptotic optimality result. The e-companion is available at https://doi.org/10.1287/moor.2018.0935 .
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