@article{cai_eun_2009, title={Crossing Over the Bounded Domain: From Exponential to Power-Law Intermeeting Time in Mobile Ad Hoc Networks}, volume={17}, ISSN={["1558-2566"]}, DOI={10.1109/TNET.2008.2011734}, abstractNote={Intermeeting time between mobile nodes is one of the key metrics in a mobile ad hoc network (MANET) and central to the end-to-end delay of forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: The intermeeting time distribution, in fact, follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution of the intermeeting time and, thus, calls for further study on the power-law intermeeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the intermeeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the intermeeting time. We then discuss the relationship between the size of the boundary and the relevant timescale of the network scenario under consideration. Our results thus provide guidelines on the mobility modeling with power-law intermeeting time distribution, new protocols including packet-forwarding algorithms, as well as their performance analysis.}, number={5}, journal={IEEE-ACM TRANSACTIONS ON NETWORKING}, author={Cai, Han and Eun, Do Young}, year={2009}, month={Oct}, pages={1578–1591} }
 @article{won_cai_eun_guo_netravali_rhee_sabnani_2009, title={Multicast Scheduling in Cellular Data Networks}, volume={8}, ISSN={["1558-2248"]}, DOI={10.1109/twc.2009.080330}, abstractNote={Multicast is an efficient means of transmitting the same content to multiple receivers while minimizing network resource usage. Applications that can benefit from multicast such as multimedia streaming and download, are now being deployed over 3G wireless data networks. Existing multicast schemes transmit data at a fixed rate that can accommodate the farthest located users in a cell. However, users belonging to the same multicast group can have widely different channel conditions. Thus existing schemes are too conservative by limiting the throughput of users close to the base station. We propose two proportional fair multicast scheduling algorithms that can adapt to dynamic channel states in cellular data networks that use time division multiplexing: Inter-group Proportional Fairness (IPF) and multicast proportional fairness (MPF). These scheduling algorithms take into account (1) reported data rate requests from users which dynamically change to match their link states to the base station, and (2) the average received throughput of each user inside its cell. This information is used by the base station to select an appropriate data rate for each group. We prove that IPF and MPF achieve proportional fairness among groups and among all users in a group inside a cell respectively. Through extensive packet-level simulations, we demonstrate that these algorithms achieve good balance between throughput and fairness among users and groups.}, number={9}, journal={IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS}, author={Won, Hyungsuk and Cai, Han and Eun, Do Young and Guo, Katherine and Netravali, Arun and Rhee, Injong and Sabnani, Krishan}, year={2009}, month={Sep}, pages={4540–4549} }
 @article{cai_eun_ha_rhee_xu_2009, title={Stochastic convex ordering for multiplicative decrease internet congestion control}, volume={53}, ISSN={["1872-7069"]}, DOI={10.1016/j.comnet.2008.10.012}, abstractNote={Window growth function for congestion control is a strong determinant of protocol behaviors, especially its second and higher-order behaviors associated with the distribution of transmission rates, its variances, and protocol stability. This paper presents a new stochastic tool, called convex ordering, that provides an ordering of any convex function of transmission rates of two multiplicative-decrease protocols and valuable insights into high-order behaviors of protocols. As the ordering determined by this tool is consistent with any convex function of rates, it can be applied to any unknown metric for protocol performance that consists of some high-order moments of transmission rates, as well as those already known such as rate variance. Using the tool, it is analyzed that a protocol with a growth function that starts off with a concave function and then switches to a convex function (e.g., an odd order function such as x3 and x5) around the maximum window size in the previous loss epoch, gives the smallest rate variation under a variety of network conditions. Among existing protocols, BIC and CUBIC have this window growth function. Experimental and simulation results confirm the analytical findings.}, number={3}, journal={COMPUTER NETWORKS}, author={Cai, Han and Eun, Do Young and Ha, Sangtae and Rhee, Injong and Xu, Lisong}, year={2009}, month={Feb}, pages={365–381} }
 @article{cai_lee_eun_2008, title={Invariance property of isotropic random walk mobility patterns in mobile ad-hoc networks}, ISBN={["978-1-4244-2074-2"]}, ISSN={["1550-3607"]}, DOI={10.1109/icc.2008.410}, abstractNote={The class of isotropic random walk mobility models, including random direction mobility model, random walk mobility model and Brownian motion mobility model, has been widely used in the study of Mobile Ad-Hoc Networks for mobility modeling and control. In this paper, we show an important property for contact time of isotropic random walk mobility models. Specifically, we find that the mean contact time of two mobile nodes following isotropic random walk mobility models is invariant with respect to the step-length distribution under both the simplest distance-based (Boolean) interference model and the more realistic SINR-based interference model. We also study the effect of system parameters on the contact and inter-meeting time of mobile nodes and discuss their higher-order statistics.}, journal={2008 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS, PROCEEDINGS, VOLS 1-13}, author={Cai, Han and Lee, Chul-Ho and Eun, Do Young}, year={2008}, pages={2141–2145} }
 @article{cai_eun_2008, title={Tuning up the performance of constant-time distributed scheduling algorithms via majorization}, ISBN={["978-1-4244-2074-2"]}, ISSN={["1550-3607"]}, DOI={10.1109/icc.2008.552}, abstractNote={Scheduling algorithms assign contention probability for each link in wireless ad hoc networks and plays a key role in deciding the system performance. Recently, many low-cost distributed scheduling algorithms are proposed. In this paper, we propose to improve the performance of a class of distributed collision-based scheduling algorithms, called constant-time distributed scheduling algorithms, by exploring the advantage brought by the unevenness of links' contention probabilities. Specifically, we prove that there exists ordering relationship for the success probability of any neighborhood when the contention probability vectors are ordered in the sense of majorization. We show how to modify the existing algorithms so as to find a new contention probability vector that majorizes the original one in a distributed manner. Our simulation results indicate that by using our modified algorithms, the average queue-lengths of a stable system can be reduced by 25% to 50%, while the capacity region remains the same. Our modification to the existing algorithms is extremely simple and entails essentially zero additional cost.}, journal={2008 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS, PROCEEDINGS, VOLS 1-13}, author={Cai, Han and Eun, Do Young}, year={2008}, pages={2931–2935} }