The Vehicle Routing Problem (VRP) is a discrete optimization problem with high industrial relevance and high computational complexity. The problem has been extensively studied since it was introduced by Dantzig and Ramser. In a VRP, we are given a number of customers with known delivery requirements and locations (assumed to be vertices in a network). A fleet of vehicles with limited capacity is available. The objective is to design routes and customer assignments to minimize the total time or distance traveled to serve the demands. Because of its practical significance, this problem has been widely studied.
\r\n\r\nIn this thesis, we present a version of the VRP motivated by mobile sensor networks which we call the Capacitated Multivehicle Routing Problem (CMVRP). In our framework, there are multiple geographically disperse vehicles each equipped with a limited energy supply. The vehicle consumes energy as it moves around and it also consumes energy while serving jobs. This situation models a network of mobile sensors where locomotion and computation all drain the limited capacity battery onboard. Our objective is to determine the minimum amount of energy required to serve all jobs, which takes into account both the service requirement and the travel overhead. We present a constant factor approximation algorithm. Furthermore, we study the on-line problem where job demands arrive sequentially and present a distributed algorithm that serves all jobs using only a constant factor more energy than the off-line solution.
", "doi": "10.7907/3Y9X-EW47", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:2582", "collection": "thesis", "collection_id": "2582", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06142004-161237", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 2027590, "license": "other", "mime_type": "application/pdf", "url": "/2582/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Router Congestion Control", "author": [ { "family_name": "Gao", "given_name": "Xiaojie", "clpid": "Gao-Xiaojie" } ], "thesis_advisor": [ { "family_name": "Schulman", "given_name": "Leonard J.", "clpid": "Schulman-L-J" } ], "thesis_committee": [ { "family_name": "Unknown", "given_name": "Unknown" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Congestion is a natural phenomenon in any network queuing system, and is unavoidable if the queuing system is operated at capacity. In this thesis, we study how to set the rules of a queuing system so that all the users have a self interest in controlling congestion when it happens.
\r\n\r\nQueueing system is a crucial component in effective router congestion control since it determines the way packets from different sources interact with each other. If packets are dropped by the queueing system indiscriminately, in some cases, the effect can be to encourage senders to actually increase their transmission rates, worsening the congestion, and destabilizing the system.
\r\n\r\nWe approach this problem from game theory. We look on each flow as a competing player in the game; each player is trying to get as much bandwidth as possible. Our task is to design a game at the router that will protect low-volume flows and punish high-volume ones. Because of the punishment, being high-volume will be counter productive, so flows will tend to use a responsive protocol as their transport-layer protocol. The key aspect of our solution is that by sending no packets from high-volume flows in case of congestion, it gives these flows an incentive to use a more responsive protocol.
\r\n\r\nIn the thesis, we will describe several implementations of our solution, and show that we achieve the desired game-theoretic equilibrium while also maintaining bounded queue lengths and responding to changes in network flow conditions. Finally, we accompany the theoretical analysis with network simulations under a variety of conditions.
\r\n", "doi": "10.7907/VZ4D-4047", "publication_date": "2004", "thesis_type": "masters", "thesis_year": "2004" } ]