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Understanding the Fundamentals of Empty-Car Routing in Ridesharing Systems How to efficiently route empty-cars in ridesharing systems? In this paper “Empty-car Routing in Ridesharing Systems,” A. Braverman, J.G. Dai, X. Liu, and L. Ying introduce a novel model based on closed queueing networks and propose an optimization framework to optimize empty-car routing for maximizing system-wide utility functions. We propose a fluid-based optimal routing policy by solving the optimization problem in a large market regime. We establish both process-level and steady-state convergence of the closed queueing network to the fluid-limit and prove the optimal network utility obtained from the fluid-based optimization is an upper bound on the utility in the finite car system for any routing policy under which the closed queueing network has a stationary distribution. This upper bound is achieved asymptotically under the fluid-based optimal routing policy. This paper considers a closed queueing network model of ridesharing systems, such as Didi Chuxing, Lyft, and Uber. We focus on empty-car routing, a mechanism by which we control car flow in the network to optimize system-wide utility functions, for example, the availability of empty cars when a passenger arrives. We establish both process-level and steady-state convergence of the queueing network to a fluid limit in a large market regime where demand for rides and supply of cars tend to infinity and use this limit to study a fluid-based optimization problem. We prove that the optimal network utility obtained from the fluid-based optimization is an upper bound on the utility in the finite car system for any routing policy, both static and dynamic, under which the closed queueing network has a stationary distribution. This upper bound is achieved asymptotically under the fluid-based optimal routing policy. Simulation results with real-world data released by Didi Chuxing demonstrate the benefit of using the fluid-based optimal routing policy compared with various other policies.

Time reversibility is used to prove Burke's theorem, which, in turn is used to show that the queues in feed‐forward networks, with Poisson inputs and random routing, have joint probability distribution of number of messages in queues as that of all independent M/M/S queues(product form). By deriving a multi‐dimensional Kolmogorov equation it is shown that the result applies to open networks with feedback satisfying certain general conditions. These are the Jackson networks. The result is used to find the average delay in networks, given routing and input flows to the network. The average delay is minimized by an optimum allocation of capacity in the links in the network. The same results are then derived for closed networks of queues. The next step in the development is extending the model from FCFS nodes with exponential servers to arbitrary service and the processor sharing, infinite service and LCFS disciplines. The results are applied to forward packet switching nodes, window flow control and cellular wireless.

We analyze a novel two-level queueing network with blocking, consisting of N level-1 parallel queues linked toM level-2 parallel queues. The processing of a customer by a level-1 server requires additional services that are exclusively offered by level-2 servers. These level-2 servers are accessed through blocking and non-blocking messages issued by level-1 servers. If a blocking message is issued, the level-1 server gets blocked until the message is fully processed at the level-2 server. The queueing network is analyzed approximately using a decomposition method, which can be viewed as a generalization of the well-known twonode decomposition algorithm used to analyze tandem queueing networks with blocking. Numerical tests show that the algorithm has a good accuracy. [PUBLICATION ABSTRACT]