arXiv subjects

Shreehari Anand Bodas

Publications and source records attributed to Shreehari Anand Bodas.

4 recordsLinked to original sources

arXiv2026

Dynamic Core Allocation for Malleable Jobs with Unknown Speed-up Parameters

We study dynamic resource allocation in a multicore computing system with a fixed number of processing cores and a stream of malleable jobs. Each job may adjust its level of parallelism during execution, allowing adaptive redistribution of resources across concurrently active jobs. Jobs belong to one of two observable classes, each characterized by a distinct speed-up function with unknown parameters. The objective is to learn a core-allocation policy that minimizes the long-run mean number of jobs in the system, equivalently the mean response time in steady state. \noindent To address this uncertainty, we develop an iterative learning-and-control framework. The system alternates between estimating the unknown speed-up parameters from observed job completions and solving the associated Markov decision process (MDP) to update the allocation policy. Within each job class, cores are shared equally among active jobs; the fraction of capacity assigned to each class is obtained from the MDP formulation of \cite{berg2017}, evaluated at the current parameter estimates. We construct a maximum likelihood estimator based on state-dependent inter-departure times and prove its strong consistency under a fixed allocation policy. We further propose two learning algorithms that combine this estimation step with dynamic programming-based policy updates, and illustrate their through numerical experiments.

math.OC↗

arXiv2026

A stochastic optimization algorithm for revenue maximization in a service system with balking customers

This paper analyzes a service system modeled as a single-server queue, in which the service provider aims to dynamically maximize the expected revenue per unit of time. This is achieved by constructing a stochastic gradient descent algorithm that dynamically adjusts the price. A key feature of our modeling framework is that customers may choose to balk - that is, decide not to join - when facing high congestion. A notable strength of our approach is that the revenue-maximizing algorithm relies solely on information about effective arrivals, meaning that only the behavior of customers who choose not to balk is observable and used in decision-making. This results in an elaborate interplay between the pricing policy and the effective arrival process, yielding a non-standard state dependent queueing process. An important contribution of our work concerns a novel Infinitesimal Perturbation Analysis (IPA) procedure that is able to consistently estimate the stationary effective arrival rate. This is further leveraged to construct an iterative algorithm that converges, under mild regularity conditions, to the optimal price with provable asymptotic guarantees.

math.OC↗

arXiv2025

Useful stochastic bounds in time-varying queues with service and patience times having general joint distribution

Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $λ:[0,\infty)\rightarrow[0,λ_h ]$ for some $λ_h>0$. For each $i\in\mathbb{N}$, let $S_i$ (resp., $Y_i$) be the service (resp., patience) time of the $i$'th customer and assume that $(S_1,Y_1),(S_2,Y_2),\ldots$ is an iid sequence of bivariate random vectors with non-negative coordinates. A customer joins if and only if his patience time is not less than his prospective waiting time (i.e., the left-limit of the workload process at his arrival epoch). Let $τ(x)$ be the first time when the system becomes empty and let $N^*_λ(\cdot)$ be the arrival process of those who join the queue. In the present work we suggest a novel coupling technique which is applied to derive stochastic upper bounds for the functionals: \begin{equation*} \int_0^{τ(x)}g\circ W_x(t){\rm d}t\ \ \text{and}\ \ \int_0^{τ(x)}g\circ W_x(t){\rm d}N^*_λ(t)\,, \end{equation*} where $W_x(\cdot)$ is the workload process in the queue and $g(\cdot)$ is any lower semi-continuous function. We also demonstrate how to utilise these bounds via some examples under the additional assumption that $λ(\cdot)$ is periodic.

math.PR↗

arXiv2024

Statistical inference for a service system with non-stationary arrivals and unobserved balking

We study a multi-server queueing system with a periodic arrival rate and customers whose joining decision is based on their patience and a delay proxy. Specifically, each customer has a patience level sampled from a common distribution. Upon arrival, they receive an estimate of their delay before joining service and then join the system only if this delay is not more than their patience, otherwise they balk. The main objective is to estimate the parameters pertaining to the arrival rate and patience distribution. Here the complication factor is that this inference should be performed based on the observed process only, i.e., balking customers remain unobserved. We set up a likelihood function of the state dependent effective arrival process (i.e., corresponding to the customers who join), establish strong consistency of the MLE, and derive the asymptotic distribution of the estimation error. Due to the intrinsic non-stationarity of the Poisson arrival process, the proof techniques used in previous work become inapplicable. The novelty of the proving mechanism in this paper lies in the procedure of constructing i.i.d. objects from dependent samples by decomposing the sample path into i.i.d. regeneration cycles. The feasibility of the MLE-approach is discussed via a sequence of numerical experiments, for multiple choices of functions which provide delay estimates. In particular, it is observed that the arrival rate is best estimated at high service capacities, and the patience distribution is best estimated at lower service capacities.

math.PR↗