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We study the max-min fairness of multi-task jobs in distributed computing platforms. We consider a setting where each job consists of a set of parallel tasks that need to be processed on different servers, and the job is completed once all its tasks finish processing. Each job is associated with a utility which is a decreasing function of its completion time, and captures how sensitive it is to latency. The objective is to schedule tasks in a way that achieves max-min fairness for jobs' utilities, i.e., an optimal schedule in which any attempt to improve the utility of a job necessarily results in hurting the utility of some other job with smaller or equal utility. We first show a strong result regarding NP-hardness of finding the max-min fair vector of job utilities. The implication of this result is that achieving max-min fairness in many other distributed scheduling problems (e.g., coflow scheduling) is NP-hard. We then proceed to define two notions of approximation solutions: one based on finding a certain number of elements of the max-min fair vector, and the other based on a single-objective optimization whose solution gives the max-min fair vector. We develop scheduling algorithms that provide guarantees under these approximation notions, using dynamic programming and random perturbation of tasks' processing times. We verify the performance of our algorithms through extensive simulations, using a real traffic trace from a large Google cluster. 

We study the max-min fairness of multi-task jobs in distributed computing platforms. We consider a setting where each job consists of a set of parallel tasks that need to be processed on different servers, and the job is completed once all its tasks finish processing. Each job is associated with a utility which is a decreasing function of its completion time, and captures how sensitive it is to latency. The objective is to schedule tasks in a way that achieves max-min fairness for jobs’ utilities, i.e., an optimal schedule in which any attempt to improve the utility of a job necessarily results in hurting the utility of some other job with smaller or equal utility.We first show a strong result regarding NP-hardness of finding the max-min fair vector of job utilities. The implication of this result is that achieving max-min fairness in many other distributed scheduling problems (e.g., coflow scheduling) is NP-hard. We then proceed to define two notions of approximation solutions: one based on finding a certain number of elements of the max-min fair vector, and the other based on a single-objective optimization whose solution gives the max-min fair vector. We develop scheduling algorithms that provide guarantees under these approximation notions, using dynamic programming and random perturbation of tasks’ processing times. We verify the performance of our algorithms through extensive simulations, using a real traffic trace from a large Google cluster. 

WiFi is the dominant means for home Internet access, yet is frequently a performance bottleneck. Without reliable, satisfactory performance at the last hop, end-to-end quality of service (QoS) efforts will fail. Three major reasons for WiFi bottlenecking performance are its: 1) inherent wireless channel characteristics, 2) approach to access control of the shared broadcast channel, and 3) impact on transport layer protocols, such as TCP, that operate end-to-end, and over-react to the loss or delay caused by the single WiFi link. In this paper, we leverage the philosophy of centralization in modern networking and present our cross layer design to address the problem. Specifically, we introduce centralized control at the point of entry/egress into the WiFi network. Based on network conditions measured from buffer sizes, airtime and throughput, flows are scheduled to the optimal utility. Unlike most existing WiFi QoS approaches, {\em our design only relies on transparent modifications, requiring no changes to the network (including link layer) protocols, applications, or user intervention}. Through extensive experimental investigation, we show that our design significantly enhances the reliability and predictability of WiFi performance, providing a ``virtual wire''-like link to the targeted application. 

Full-duplex (FD) wireless is an attractive communication paradigm with high potential for improving network capacity and reducing delay in wireless networks. Despite significant progress on the physical layer development, the challenges associated with developing medium access control (MAC) protocols for heterogeneous networks composed of both legacy half-duplex (HD) and emerging FD devices have not been fully addressed. In [1], we focused on the design and performance evaluation of scheduling algorithms for heterogeneous HD-FD networks and presented the distributed Hybrid-Greedy Maximal Scheduling (H-GMS) algorithm. H-GMS combines the centralized Greedy Maximal Scheduling (GMS) and a distributed queue-based random-access mechanism, and is throughput-optimal. In this paper, we analyze the delay performance of H-GMS by deriving two lower bounds on the average queue length. We also evaluate the fairness and delay performance of H-GMS via extensive simulations. We show that in heterogeneous HD-FD networks, H-GMS achieves$16-30\times$ better delay performance and improves fairness between FD and HD users by up to 50% compared with the fully decentralized Q-CSMA algorithm.