Online Routing Games (with Online Real-time Data) László Z. Varga 1
Road Traffic: Routing Problem 2
Road Traffic: Routing Game 2 1 3
Road Traffic: Autonomous • A centralized system would be able to create an optimal plan for the trips of the cars • optimality: for some ''global'' parameter • fairness: e.g. none of the cars pays with some extra long travel time for the global optimum • Autonomous: • traffic participants make autonomous decisions based on their intentions and the information available for them locally • Individually self-optimizing travel routes does not necessarily result in optimal traffic 4
Algorithmic Game Theory (Routing Games) • Algorithmic game theory studies networks with source routing • The price of anarchy and its properties by Roughgarden and Tardos • Important basic properties understood: • Nonatomic routing problem has at least one equilibrium flow distribution and all equilibrium flow distributions have the same total cost • Price of anarchy is the ratio between the cost of an equilibrium flow distribution and the optimal flow distribution • Upper bound on the price of anarchy • The flow distribution converges to an equilibrium 5
Road Traffic: Online Real-time Data • Decision is based on current situation, which may change while they are on route 2 1 6
Road Traffic: Online Real-time Data • Decision is based on current situation, and they may get there at different times 2 1 7
Road Traffic: Online Real-time Data • Subsequent agents of the same flow may select different routes 2 1 8
Online Real-time Data: Beyond Routing Games • a) the throughput characteristic of the network may change with time and the drivers cannot compute or learn this characteristic by repeatedly passing the road network; • b) there is no flow level route selection, because drivers continuously enter the road network and decide their optimal route when they enter the road network and the decision is based on the live information on the current situation of the road network; and • c) the outcome travel time for a given driver depends on the trip schedule of some other drivers that entered the network previously, are currently entering the network or will enter the network later. 9
Novel Model: Online Routing Games L á szl ó Z. Varga: Online Routing • (t, T, G, c, r, k) sextuple, where Games and the Benefit of Online Data, in Proc. Eighth International • t={1, 2, ...} sequence of time periods; Workshop on Agents in Traffic and Transportation, at 13th Int. Conf. on • T time periods giving one time unit; Autonomous Agents and Multiagent Systems (AAMAS 2014), May 5-6, 2014, Paris, France, pp. 88-95. • G is a directed graph G=(V, E) • c is the cost function of G with c e :R + →R + • r total flow, r i aiming for a P i trip from s i to t i • k=(k 1 , k 2 ,…) sequence of decision vectors with k t =(k t 1 , k t 2 ,…) decision vector made in time period t and k t i the decision made by the agent of the r i flow in time period t 10
Novel Model: Online Routing Games • the variable part of the c e cost functions are not known to any of the agents of the model • and the agents can learn the actual cost only when an agent exits an edge and reports it • the actual cost of a path (e 1 , e 2 , e 3 , …) for a flow starting at time period t is determined at the time when the flow enters each edge 11
Benefit of Online Real-time Data • Definition 1. The worst case benefit of online real time data at a given flow is the ratio between the cost of the maximum cost of the flow and the cost of the same flow with an oracle using the same decision making strategy and only the fixed part of the cost functions. • Definition 2. The best case benefit of … • Definition 3. The average case benefit of … 12
Simple Naive Online Routing Games • Typical navigation software use shortest path search, we call this decision strategy as simple naïve strategy • It is proved that in simple naive online routing games: • equlibrium is not guaranteed • single flow intensification may happen • worst case benefit may be more than 1 13
Anticipatory Vehicle Routing, Intention Propagation • a vehicle agent running on a smart device inside the vehicle • vehicle agents communicate their individual planned route to delegate MAS • the delegate MAS makes forecast of future traffic density • the delegate MAS sends back the traffic forecast to the vehicle agents which use this information to plan their trip R. Claes, T. Holvoet, and D. Weyns: A decentralized approach for anticipatory vehicle routing using delegate multi-agent systems, in IEEE Transactions on Intelligent Transportation Systems, vol. 12, no. 2, pp. 364-373, 2011 14
SNIP Online Routing Games • Simple naive intention propagation online routing games are online routing games where • the decision making agents of the flows are the vehicle agents • the delegate MAS predicts the travel times for each path of the trip • the decision is to select the path with the shortest predicted travel time • It is proved that László Zsolt Varga: On Intention- in SNIP online routing games: Propagation-Based Prediction in Autonomously Self-adapting • equlibrium is not guaranteed Navigation; Scalable Computing: Practice And Experience 16:(3) pp. • single flow intensification may happen 221-232. (2015) • worst case benefit may be more than 1 15
Conclusions • A theoretical model for the metric and analysis of autonomous navigation based on online data • We have shown that autonomous self-adaptation with these strategies • sometimes make the system fluctuate, • sometimes some agents pay a price for the autonomous self-adaptation of the whole system, • Intention-sharing-based prediction is a form of cooperation, which helps to solve these problems, but the proof is still a research challenge 16
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