Resource augmentation in load balancing

We consider load-balancing in the following setting. The on-line algorithm is allowed to use $n$ machines, whereas the optimal off-line algorithm is limited to $m$ machines, for some fixed $m < n$. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of $n/m$, the best on-line algorithm has a ratio which decays exponentially in $n/m$. Specifically, we give an algorithm with competitive ratio of 1+2^{- frac{n{m (1- o (1)), and a lower bound of 1+ e^{ - frac{n{m (1+ o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1+ e^{ - frac{n{m (1+ o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for $n=m+1$, the greedy algorithm is optimal. (It is not optimal for permanent tasks.

Rejecting Jobs to Minimize Load and Maximum Flow-time

Online algorithms are usually analyzed using the notion of competitive ratio which compares the solution obtained by the algorithm to that obtained by an online adversary for the worst possible input sequence. Often this measure turns out to be too pessimistic, and one popular approach especially for scheduling problems has been that of "resource augmentation" which was first proposed by Kalyanasundaram and Pruhs. Although resource augmentation has been very successful in dealing with a variety of objective functions, there are problems for which even a (arbitrary) constant speedup cannot lead to a constant competitive algorithm. In this paper we propose a "rejection model" which requires no resource augmentation but which permits the online algorithm to not serve an epsilon-fraction of the requests. The problems considered in this paper are in the restricted assignment setting where each job can be assigned only to a subset of machines. For the load balancing problem where the objective is to minimize the maximum load on any machine, we give O(\log^2 1/\eps)-competitive algorithm which rejects at most an \eps-fraction of the jobs. For the problem of minimizing the maximum weighted flow-time, we give an O(1/\eps^4)-competitive algorithm which can reject at most an \eps-fraction of the jobs by weight. We also extend this result to a more general setting where the weights of a job for measuring its weighted flow-time and its contribution towards total allowed rejection weight are different. This is useful, for instance, when we consider the objective of minimizing the maximum stretch. We obtain an O(1/\eps^6)-competitive algorithm in this case. Our algorithms are immediate dispatch, though they may not be immediate reject. All these problems have very strong lower bounds in the speed augmentation model

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201

Online Makespan Minimization with Parallel Schedules

In online makespan minimization a sequence of jobs $\sigma = J_1,..., J_n$ has to be scheduled on $m$ identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new model of resource augmentation. Here, an online algorithm is allowed to build several schedules in parallel while processing $\sigma$. At the end of the scheduling process the best schedule is selected. This model can be viewed as providing an online algorithm with extra space, which is invested to maintain multiple solutions. The setting is of particular interest in parallel processing environments where each processor can maintain a single or a small set of solutions. We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a (1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value depends on $m$ but is independent of the input $\sigma$. The performance guarantees are nearly best possible. We show that any algorithm that achieves a competitiveness smaller than 4/3 must construct $\Omega(m)$ schedules. Our algorithms make use of novel guessing schemes that (1) predict the optimum makespan of a job sequence $\sigma$ to within a factor of 1+\eps and (2) guess the job processing times and their frequencies in $\sigma$. In (2) we have to sparsify the universe of all guesses so as to reduce the number of schedules to a constant. The competitive ratios achieved using parallel schedules are considerably smaller than those in the standard problem without resource augmentation

Fog Computing: A Taxonomy, Survey and Future Directions

In recent years, the number of Internet of Things (IoT) devices/sensors has increased to a great extent. To support the computational demand of real-time latency-sensitive applications of largely geo-distributed IoT devices/sensors, a new computing paradigm named "Fog computing" has been introduced. Generally, Fog computing resides closer to the IoT devices/sensors and extends the Cloud-based computing, storage and networking facilities. In this chapter, we comprehensively analyse the challenges in Fogs acting as an intermediate layer between IoT devices/ sensors and Cloud datacentres and review the current developments in this field. We present a taxonomy of Fog computing according to the identified challenges and its key features.We also map the existing works to the taxonomy in order to identify current research gaps in the area of Fog computing. Moreover, based on the observations, we propose future directions for research

MAGDA: A Mobile Agent based Grid Architecture

Mobile agents mean both a technology and a programming paradigm. They allow for a flexible approach which can alleviate a number of issues present in distributed and Grid-based systems, by means of features such as migration, cloning, messaging and other provided mechanisms. In this paper we describe an architecture (MAGDA – Mobile Agent based Grid Architecture) we have designed and we are currently developing to support programming and execution of mobile agent based application upon Grid systems

Multi-processor Scheduling to Minimize Flow Time with epsilon Resource Augmentation

We investigate the problem of online scheduling of jobs to minimize flow time and stretch on m identical machines. We consider the case where the algorithm is given either (1 + ε)m machines or m machines of speed (1 + ε), for arbitrarily small ε \u3e 0. We show that simple randomized and deterministic load balancing algorithms, coupled with simple single machine scheduling strategies such as SRPT (shortest remaining processing time) and SJF (shortest job first), are O(poly(1/ε))-competitive for both flow time and stretch. These are the first results which prove constant factor competitive ratios for flow time or stretch with arbitrarily small resource augmentation. Both the randomized and the deterministic load balancing algorithms are non- migratory and do immediate dispatch of jobs. The randomized algorithm just allocates each incoming job to a random machine. Hence this algorithm is non- clairvoyant, and coupled with SETF (shortest elapsed time first), yields the first non-clairvoyant algorithm which is con- stant competitive for minimizing flow time with arbitrarily small resource augmentation. The deterministic algorithm that we analyze is due to Avrahami and Azar. For this algorithm, we show O(1/ε)-competitiveness for total flow time and stretch, and also for their Lp norms, for any fixed p ≥ 1