arXiv subjects

Rahul Vaze

Publications and source records attributed to Rahul Vaze.

At least 37 records · Page 2Linked to original sources

arXiv2023

On Dynamic Regret and Constraint Violations in Constrained Online Convex Optimization

A constrained version of the online convex optimization (OCO) problem is considered. With slotted time, for each slot, first an action is chosen. Subsequently the loss function and the constraint violation penalty evaluated at the chosen action point is revealed. For each slot, both the loss function as well as the function defining the constraint set is assumed to be smooth and strongly convex. In addition, once an action is chosen, local information about a feasible set within a small neighborhood of the current action is also revealed. An algorithm is allowed to compute at most one gradient at its point of choice given the described feedback to choose the next action. The goal of an algorithm is to simultaneously minimize the dynamic regret (loss incurred compared to the oracle's loss) and the constraint violation penalty (penalty accrued compared to the oracle's penalty). We propose an algorithm that follows projected gradient descent over a suitably chosen set around the current action. We show that both the dynamic regret and the constraint violation is order-wise bounded by the {\it path-length}, the sum of the distances between the consecutive optimal actions. Moreover, we show that the derived bounds are the best possible.

cs.LG↗

arXiv2022

Non-asymptotic near optimal algorithms for two sided matchings

A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served immediately upon arrival get blocked, as well as a queueing model, wherein customers wait in a queue until they receive service. The objective is to maximize the platform profit generated from matching servers and customers, subject to quality of service constraints, such as the expected wait time of servers in the loss system model, and the stability of the customer queue in the queuing model. For the loss system, subject to a certain relaxation, we show that the optimal policy has a bang-bang structure. We also derive approximation guarantees for simple pricing policies. For the queueing system, we propose a simple bi-modal matching strategy and show that it achieves near optimal profit.

math.OC↗

arXiv2022

Minimizing Age of Information under Arbitrary Arrival Model with Arbitrary Packet Size

We consider a single source-destination pair, where information updates arrive at the source at arbitrary time instants. For each update, its size, i.e. the service time required for complete transmission to the destination, is also arbitrary. At any time, age of information (AoI) is equal to the difference between the current time, and the arrival time of the latest update (at the source) that has been completely transmitted (to the destination). AoI quantifies the staleness of the update (information) at the destination. The goal is to find a causal scheduling policy that minimizes the time average of AoI, where the possible decisions at any time are i) whether to preempt the update under transmission upon arrival of a new update, and ii) if no update is under transmission, then choose which update to transmit (among the available updates). In this paper, we propose a causal policy called SRPT$^+$ that at each time, i) preempts the update under transmission if a new update arrives with a smaller size, and ii) if no update is under transmission, then begins to transmit the update for which the ratio of the reduction in AoI upon complete transmission (if not preempted in future) and the remaining size, is maximum. We characterize the performance of SRPT$^+$ using the metric called the competitive ratio, i.e. the ratio of the average AoI of causal policy and the average AoI of an optimal offline policy (that knows the entire input in advance), maximized over all possible inputs. We show that the competitive ratio of SRPT$^+$ is at most $4$. Further, we propose a simpler policy called SRPT$^L$, that i) preempts the update under transmission if a new update arrives with a smaller size, and ii) if no update is under transmission, then begins to transmit the update with the latest arrival time. We show that the competitive ratio of SRPT$^L$ is at most $29$.

cs.IT↗

arXiv2022

Scheduling for Multi-Phase Parallelizable Jobs

With multiple identical unit speed servers, the online problem of scheduling jobs that migrate between two phases, limitedly parallelizable or completely sequential, and choosing their respective speeds to minimize the total flow time is considered. In the limited parallelizable regime, allocating $k$ servers to a job, the speed extracted is $k^{1/α}, α>1$, a sub-linear, concave speedup function, while in the sequential phase, a job can be processed by at most one server with a maximum speed of unity. A LCFS based algorithm is proposed for scheduling jobs which always assigns equal speed to the jobs that are in the same phase (limitedly parallelizable/sequential), and is shown to have a constant (dependent only on $α> 1$) competitive ratio. For the special case when all jobs are available beforehand, improved competitive ratio is obtained.

cs.DS↗

arXiv2022

Scheduling to Minimize Age of Information with Multiple Sources

We consider a G/G/1 queueing system with a single server, where updates arrive from different sources stochastically with possibly different update inter-generation time distributions. The server can transmit/serve at most one update at any time, with potentially different transmission/service times for updates belonging to distinct sources. The age of information (AoI) of any source is a function of the time difference between the departure time of successive updates of that source. Each fully/partially transmitted update incurs a fixed (energy) cost, and the goal of the scheduler is to minimize the linear combination of the sum of the age of information across all sources and the total energy cost. We propose a simple non-preemptive randomized scheduling algorithm that randomly marks arriving updates from a source to be eligible for transmission with a fixed probability and discards them otherwise. Every time the server becomes free, it chooses a source for transmission randomly with another fixed probability and begins to transmit the most recently marked update of the chosen source. Both the respective probabilities are chosen by solving a convex program. The competitive ratio of the proposed algorithm (against a non-preemptive offline optimal algorithm) is shown to be 3 plus the maximum of the ratio of the variance and the mean of the inter-arrival time distribution of sources. For several common distributions such as exponential, uniform and Rayleigh, the competitive ratio is at most 4. For preemptive policies, a G/M/1 system is considered and a non-preemptive policy is shown to have competitive ratio (against a preemptive offline optimal algorithm) at most 5 plus the maximum of the ratio of the variance and the mean of the inter-arrival time distribution of sources.

cs.IT↗

arXiv2021

On the Age of Information of a Queuing System with Heterogeneous Servers

An optimal control problem with heterogeneous servers to minimize the average age of information (AoI) is considered. Each server maintains a separate queue, and each packet arriving to the system is randomly routed to one of the servers. Assuming Poisson arrivals and exponentially distributed service times, we first derive an exact expression of the average AoI for two heterogeneous servers. Next, to solve for the optimal average AoI, a close approximation is derived, called the approximate AoI, this is shown to be useful for multi-server systems as well. We show that for the optimal approximate AoI, server utilization (ratio of arrival rate and service rate) for each server should be same as the optimal server utilization with a single server queue. For two identical servers, it is shown that the average AoI is approximately 5/8 times the average AoI of a single server. Furthermore, the average AoI is shown to decrease considerably with the addition of more servers to the system.

cs.IT↗

arXiv2021

Speed Scaling with Multiple Servers Under A Sum Power Constraint

The problem of scheduling jobs and choosing their respective speeds with multiple servers under a sum power constraint to minimize the flow time + energy is considered. This problem is a generalization of the flow time minimization problem with multiple unit-speed servers, when jobs can be parallelized, however, with a sub-linear, concave speedup function $k^{1/α}, α>1$ when allocated $k$ servers, i.e., jobs experience diminishing returns from being allocated additional servers. When all jobs are available at time $0$, we show that a very simple algorithm EQUI, that processes all available jobs at the same speed is $\left(2-\frac{1}α\right) \frac{2}{\left(1-\left(\frac{1}α\right)\right)}$-competitive, while in the general case, when jobs arrive over time, an LCFS based algorithm is shown to have a constant (dependent only on $α$) competitive ratio.

cs.DS↗

arXiv2021

Speed Scaling On Parallel Servers with MapReduce Type Precedence Constraints

A multiple server setting is considered, where each server has tunable speed, and increasing the speed incurs an energy cost. Jobs arrive to a single queue, and each job has two types of sub-tasks, map and reduce, and a {\bf precedence} constraint among them: any reduce task of a job can only be processed once all the map tasks of the job have been completed. In addition to the scheduling problem, i.e., which task to execute on which server, with tunable speed, an additional decision variable is the choice of speed for each server, so as to minimize a linear combination of the sum of the flow times of jobs/tasks and the total energy cost. The precedence constraints present new challenges for the speed scaling problem with multiple servers, namely that the number of tasks that can be executed at any time may be small but the total number of outstanding tasks might be quite large. We present simple speed scaling algorithms that are shown to have competitive ratios, that depend on the power cost function, and/or the ratio of the size of the largest task and the shortest reduce task, but not on the number of jobs, or the number of servers.

cs.DS↗

arXiv2021

Minimizing the Sum of Age of Information and Transmission Cost under Stochastic Arrival Model

We consider a node-monitor pair, where updates are generated stochastically (according to a known distribution) at the node that it wishes to send to the monitor. The node is assumed to incur a fixed cost for each transmission, and the objective of the node is to find the update instants so as to minimize a linear combination of AoI of information and average transmission cost. First, we consider the Poisson arrivals case, where updates have an exponential inter-arrival time for which we derive an explicit optimal online policy. Next, for arbitrary distributions of inter-arrival time of updates, we propose a simple randomized algorithm that transmits any newly arrived update with a fixed probability (that depends on the distribution) or never transmits that update. The competitive ratio of the proposed algorithm is shown to be a function of the variance and the mean of the inter-arrival time distribution. For some of the commonly considered distributions such as exponential, uniform, and Rayleigh, the competitive ratio bound is shown to be 2.

cs.IT↗

arXiv2020

Breaking the Unit Throughput Barrier in Distributed Systems

A multi-level random power transmit strategy that is used in conjunction with a random access protocol (RAP) (e.g. ALOHA, IRSA) is proposed to fundamentally increase the throughput in a distributed communication network. A SIR model is considered, where a packet is decodable as long as its SIR is above a certain threshold. In a slot chosen for transmission by a RAP, a packet is transmitted with power level chosen according to a distribution, such that multiple packets sent by different nodes can be decoded at the receiver in a single slot, by ensuring that their SIRs are above the threshold with successive interference cancelation. Since the network is distributed this is a challenging task, and we provide structural results that aid in finding the achievable throughputs, together with upper bounds on the maximum throughput possible. The achievable throughput and the upper bounds are shown to be close with the help of comprehensive simulations. The main takeaway is that the throughput of more than 1 is possible in a distributed network, by using a judicious choice of power level distribution in conjuction with a RAP.

cs.IT↗

arXiv2020

Multiple Server SRPT with speed scaling is competitive

Can the popular shortest remaining processing time (SRPT) algorithm achieve a constant competitive ratio on multiple servers when server speeds are adjustable (speed scaling) with respect to the flow time plus energy consumption metric? This question has remained open for a while, where a negative result in the absence of speed scaling is well known. The main result of this paper is to show that multi-server SRPT can be constant competitive, with a competitive ratio that only depends on the power-usage function of the servers, but not on the number of jobs/servers or the job sizes (unlike when speed scaling is not allowed). When all job sizes are unity, we show that round-robin routing is optimal and can achieve the same competitive ratio as the best known algorithm for the single server problem. Finally, we show that a class of greedy dispatch policies, including policies that route to the least loaded or the shortest queue, do not admit a constant competitive ratio. When job arrivals are stochastic, with Poisson arrivals and i.i.d. job sizes, we show that random routing and a simple gated-static speed scaling algorithm achieves a constant competitive ratio.

cs.PF↗

arXiv2020

Non-clairvoyant Scheduling of Coflows

The coflow scheduling problem is considered: given an input/output switch with each port having a fixed capacity, find a scheduling algorithm that minimizes the weighted sum of the coflow completion times respecting the port capacities, where each flow of a coflow has a demand per input/output port, and coflow completion time is the finishing time of the last flow of the coflow. The objective of this paper is to present theoretical guarantees on approximating the sum of coflow completion time in the non-clairvoyant setting, where on a coflow arrival, only the number of flows, and their input-output port is revealed, while the critical demand volumes for each flow on the respective input-output port is unknown. The main result of this paper is to show that the proposed BlindFlow algorithm is $8p$-approximate, where $p$ is the largest number of input-output port pairs that a coflow uses. This result holds even in the online case, where coflows arrive over time and the scheduler has to use only causal information. Simulations reveal that the experimental performance of BlindFlow is far better than the theoretical guarantee.

cs.DS↗

arXiv2020

Game of Ages

We consider a distributed IoT network, where each node wants to minimize its age of information and there is a cost to make any transmission. A collision model is considered, where any transmission is successful from a node to a common monitor if no other node transmits in the same slot. There is no explicit communication/coordination between any two nodes. The selfish objective of each node is to minimize a function of its individual age of information and its transmission cost. Under this distributed competition model, the objective of this paper is to find a distributed transmission strategy for each node that converges to an equilibrium. The proposed transmission strategy only depends on the past observations seen by each node and does not require explicit information of the number of other nodes, or their strategies. A simple update strategy is shown to converge to an equilibrium, that is in fact a Nash equilibrium for a suitable utility function, that captures all the right tradeoffs for each node. In addition, the price of anarchy for the utility function is shown to approach unity as the number of nodes grows large.

cs.IT↗

arXiv2019

Throughput Maximization with an Average Age of Information Constraint in Fading Channels

In the emerging fifth generation (5G) technology, communication nodes are expected to support two crucial classes of information traffic, namely, the enhanced mobile broadband (eMBB) traffic with high data rate requirements, and ultra-reliable low-latency communications (URLLC) traffic with strict requirements on latency and reliability. The URLLC traffic, which is usually analyzed by a metric called the age of information (AoI), is assigned the first priority over the resources at a node. Motivated by this, we consider long-term average throughput maximization problems subject to average AoI and power constraints in a single user fading channel, when (i) perfect and (ii) no channel state information at the transmitter (CSIT) is available. We propose simple age-independent stationary randomized policies (AI-SRP), which allocate powers at the transmitter based only on the channel state and/or distribution information, without any knowledge of the AoI. We show that the optimal throughputs achieved by the AI-SRPs for scenarios (i) and (ii) are at least equal to the half of the respective optimal long-term average throughputs, independent of all the parameters of the problem, and that they are within additive gaps, expressed in terms of the optimal dual variable corresponding to their average AoI constraints, from the respective optimal long-term average throughputs.

cs.IT↗

arXiv2019

Online Energy Harvesting Problem Over An Arbitrary Directed Acyclic Graph Network

A communication network modelled by a directed acyclic graph (DAG) is considered, over which a source wishes to send a specified number of bits to a destination node. Each node of the DAG is powered by a separate renewable energy source, and the harvested energy is used to facilitate the source destination data flow. The challenge here is to find the optimal rate and power allocations across time for each node on its outgoing edges so as to minimize the time by which the destination receives a specified number of bits. An online setting is considered where an algorithm only has causal information about the energy arrivals. Using the competitive ratio as the performance metric, i.e. the ratio of the cost of the online algorithm and the optimal offline algorithm, maximized over all inputs, a {\it lazy} online algorithm with a competitive ratio of $2+δ$ for any $δ>0$ is proposed. Incidentally, $2$ is also a lower bound to the competitive ratio of any online algorithm for this problem. Our lazy online algorithm is described and analyzed via defining a novel max-flow problem over a DAG, where the rate on the subset of outgoing edges of any node are related/constrained. An optimal algorithm to find max-flow with these constraints is also provided, which may be of independent interest.

cs.IT↗

arXiv2019

Speed Scaling with Tandem Servers

Speed scaling for a tandem server setting is considered, where there is a series of servers, and each job has to be processed by each of the servers in sequence. Servers have a variable speed, their power consumption being a convex increasing function of the speed. We consider the worst case setting as well as the stochastic setting. In the worst case setting, the jobs are assumed to be of unit size with arbitrary (possibly adversarially determined) arrival instants. For this problem, we devise an online speed scaling algorithm that is constant competitive with respect to the optimal offline algorithm that has non-causal information. The proposed algorithm, at all times, uses the same speed on all active servers, such that the total power consumption equals the number of outstanding jobs. In the stochastic setting, we consider a more general tandem network, with a parallel bank of servers at each stage. In this setting, we show that random routing with a simple gated static speed selection is constant competitive. In both cases, the competitive ratio depends only on the power functions, and is independent of the workload and the number of servers.

cs.DS↗

arXiv2018

Not Just Age but Age and Quality of Information

A versatile scheduling problem to model a three-way tradeoff between delay/age, distortion, and energy is considered. The considered problem called the age and quality of information (AQI) is to select which packets to transmit at each time slot to minimize a linear combination of the distortion cost, the age/delay cost and the energy transmission cost in an online fashion. AQI generalizes multiple important problems such as age of information (AoI), the remote estimation problem with sampling constraint, the classical speed scaling problem among others. The worst case input model is considered, where the performance metric is the competitive ratio. A greedy algorithm is proposed that is shown to be 2-competitive, independent of all parameters of the problem. For the special case of AQI problem, a greedy online maximum weight matching based algorithm is also shown to be 2-competitive.

cs.IT↗

arXiv2018

Energy Harvesting Communications Using Dual Alternating Batteries

Practical energy harvesting (EH) based communication systems typically use a battery to temporarily store the harvested energy prior to its use for communication. The batteries can be damaged when they are repeatedly charged (discharged) after being partially discharged (charged), overcharged or deeply discharged. This motivates the cycle constraint which says that a battery must be charged (discharged) only after it is sufficiently discharged (charged). We also assume Bernoulli energy arrivals, and a half-duplex constraint due to which the batteries are not charged and discharged simultaneously. In this context, we study EH communication systems with: (a) a single-battery with capacity 2B units and (b) dual-batteries, each having capacity of B units. The aim is to obtain the best possible long-term average throughputs and throughput regions in point-to-point (P2P) channels and multiple access channels (MAC), respectively. For the P2P channel, we obtain an analytical optimal solution in the single-battery case, and propose optimal and sub-optimal power allocation policies for the dual-battery case. We extend these policies to obtain achievable throughput regions in MACs by jointly allocating rates and powers. From numerical simulations, we find that the optimal throughput in the dual-battery case is significantly higher than that in the single-battery case, although the total storage capacity in both cases is 2B units. Further, in the proposed policies, the largest throughput region in the single-battery case is contained within that of the dual-battery case.

cs.IT↗