About

Alexander L. Stolyar is a Professor in the Department of Industrial and Enterprise Systems Engineering and the Coordinated Science Lab at the University of Illinois at Urbana-Champaign. His research focuses on large-scale service systems, queueing theory, stochastic systems, and optimization in distributed and networked environments. He has made significant contributions to the understanding and analysis of complex service systems with packing constraints, flexible server pools, and multi-server systems operating under various load balancing and scheduling algorithms. His work often involves the study of asymptotic optimality, stability conditions, and large-scale behavior of stochastic networks and particle systems with mean-field interactions. Professor Stolyar's research also addresses inventory models with stochastic lead times, dynamic synchronization systems, and resource allocation in communication networks and cloud computing environments. Through his extensive publications, he has advanced theoretical foundations and practical algorithms for managing and optimizing performance in large-scale distributed systems and networks.

Research topics

• Computer Science
• Mathematics
• Mathematical optimization
• Combinatorics
• Computer network
• Operations management
• Distributed computing
• Econometrics
• Economics
• Operating system

Selected publications

• Multi-floor generalization of TASEP

  arXiv (Cornell University) · 2026-03-13

  preprintOpen accessSenior author

  We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed by a {\em back-pressure} (BP) algorithm (also often called {\em MaxWeight}). There are $N$ sites (with $N$ finite or infinite), each may contain at most $c$ particles, $1 \le c < \infty$. New particles enter the system at the left-most site $1$ as a Poisson process of rate $α\le 1$, unless site $1$ has $c$ particles. Particles (if any) are removed from the right-most site $N$ as a Poisson process of rate $β\le 1$. The left-to-right movement of particles between neighboring sites is governed by the BP rule: one particle moves from site $n$ to $n+1$ at epochs of a rate $1$ Poisson process, as long as the former site has strictly more particles than the latter. When $c=1$, this is the standard TASEP. Our main results address the asymptotics of the stationary distribution of a finite system, and especially the limit of the flux (current) as $N\to\infty$. In particular, we prove that interesting non-trivial phase transitions take place in a system with $c>1$. For example, if $c>1$ and $1/2 \le β\le 1$, the maximum limiting flux $1/4$ is achieved as long as $α\ge α_c^*$, where $α_c^* < 1/2$ is some non-trivial threshold. (For the standard TASEP the threshold is $1/2$.) We also put forward a general conjecture about the stationary distribution asymptotics under an arbitrary parameter setting. We illustrate our formal results and the conjecture by simulations, and identify interesting directions for further research.

  PublisherDOI

• Large-scale distributed synchronization systems, using a cancel-on-completion redundancy mechanism

  Queueing Systems · 2026-02-09

  articleOpen access1st authorCorresponding

  Abstract We consider a class of multi-agent distributed synchronization systems, which are modeled as n particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in Stolyar (Stoch. Syst. 12:340–372, 2022), employing so-called cancel-on-completion (c.o.c.) redundancy mechanism, but is motivated by other applications as well. In the multi-server queueing system a particle location represents a server workload. Under c.o.c. mechanism, when a job of class j arrives, it selects $$d_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:math> particles uniformly at random, which try to jump forward, by random distances, but their advance is truncated at the new location of the $$k_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:math> -th left-most selected particle ( $$k_j \le d_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> </mml:math> ). Between jumps all particles move to the left at constant speed, but cannot cross point 0 (workload cannot be less than 0). Thus, the multi-server queueing system is modeled as a particle system, regulated at the left boundary point. The more general model of this paper is such that particles evolve the same way as the in left-regulated system, but we allow regulation boundaries on either side, or both sides, or no regulation at all. We consider the mean-field asymptotic regime, when the number of particles n and the job arrival rates go to infinity, while the job arrival rates per particle remain constant. The system state for a given n is the empirical distribution of the particles’ locations. Our results include: the existence/uniqueness of fixed points of mean-field limits (ML), which describe the limiting dynamics of the system; conditions for the steady-state asymptotic independence (concentration, as $$n \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , of the stationary distribution on a single state, which is necessarily an ML fixed point); the limits, as $$n \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , of the average velocity at which unregulated (free) particle system advances. In particular, our results for the left-regulated system unify and generalize the corresponding results in Stolyar (Stoch. Syst. 12:340–372, 2022). Our technical development is such that the systems with different types of regulation are analyzed within a unified framework. In particular, these systems are used as tools for analysis of each other.

  PublisherOA PDFDOI

• Multi-floor generalization of TASEP

  arXiv (Cornell University) · 2026-03-13

  articleOpen accessSenior author

  We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed by a {\em back-pressure} (BP) algorithm (also often called {\em MaxWeight}). There are $N$ sites (with $N$ finite or infinite), each may contain at most $c$ particles, $1 \le c < \infty$. New particles enter the system at the left-most site $1$ as a Poisson process of rate $α\le 1$, unless site $1$ has $c$ particles. Particles (if any) are removed from the right-most site $N$ as a Poisson process of rate $β\le 1$. The left-to-right movement of particles between neighboring sites is governed by the BP rule: one particle moves from site $n$ to $n+1$ at epochs of a rate $1$ Poisson process, as long as the former site has strictly more particles than the latter. When $c=1$, this is the standard TASEP. Our main results address the asymptotics of the stationary distribution of a finite system, and especially the limit of the flux (current) as $N\to\infty$. In particular, we prove that interesting non-trivial phase transitions take place in a system with $c>1$. For example, if $c>1$ and $1/2 \le β\le 1$, the maximum limiting flux $1/4$ is achieved as long as $α\ge α_c^*$, where $α_c^* < 1/2$ is some non-trivial threshold. (For the standard TASEP the threshold is $1/2$.) We also put forward a general conjecture about the stationary distribution asymptotics under an arbitrary parameter setting. We illustrate our formal results and the conjecture by simulations, and identify interesting directions for further research.

  PublisherOA PDF

• Large-scale distributed synchronization systems, using a cancel-on-completion redundancy mechanism

  Queueing Systems · 2026-02-09

  articleOpen access1st authorCorresponding

  Abstract We consider a class of multi-agent distributed synchronization systems, which are modeled as n particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in Stolyar (Stoch. Syst. 12:340–372, 2022), employing so-called cancel-on-completion (c.o.c.) redundancy mechanism, but is motivated by other applications as well. In the multi-server queueing system a particle location represents a server workload. Under c.o.c. mechanism, when a job of class j arrives, it selects $$d_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:math> particles uniformly at random, which try to jump forward, by random distances, but their advance is truncated at the new location of the $$k_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:math> -th left-most selected particle ( $$k_j \le d_j$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> </mml:math> ). Between jumps all particles move to the left at constant speed, but cannot cross point 0 (workload cannot be less than 0). Thus, the multi-server queueing system is modeled as a particle system, regulated at the left boundary point. The more general model of this paper is such that particles evolve the same way as the in left-regulated system, but we allow regulation boundaries on either side, or both sides, or no regulation at all. We consider the mean-field asymptotic regime, when the number of particles n and the job arrival rates go to infinity, while the job arrival rates per particle remain constant. The system state for a given n is the empirical distribution of the particles’ locations. Our results include: the existence/uniqueness of fixed points of mean-field limits (ML), which describe the limiting dynamics of the system; conditions for the steady-state asymptotic independence (concentration, as $$n \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , of the stationary distribution on a single state, which is necessarily an ML fixed point); the limits, as $$n \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> , of the average velocity at which unregulated (free) particle system advances. In particular, our results for the left-regulated system unify and generalize the corresponding results in Stolyar (Stoch. Syst. 12:340–372, 2022). Our technical development is such that the systems with different types of regulation are analyzed within a unified framework. In particular, these systems are used as tools for analysis of each other.

  PublisherOA PDFDOI

• New Policies Exploiting Randomness of Lead Times in Inventory Systems

  Naval Research Logistics (NRL) · 2025-07-09

  articleOpen access1st authorCorresponding

  ABSTRACT Recent research provided proof‐of‐concept that the randomness of lead times in inventory systems can be exploited to achieve large—potentially unlimited—performance improvements, compared to the case of constant lead time. Specifically, the Generalized Base Stock (GBS) policy serves as such proof‐of‐concept—it can deliver unlimited improvements within a certain class of models, when the ratio of the minimum lead time to the mean lead time can be arbitrarily small. In this paper, we explore what improvements are actually achievable under practical system constraints, most importantly—in discrete‐time systems, where the minimum‐to‐mean lead time ratio is lower bounded by a positive constant; and also, which policies both allow significant improvements and are attractive for practical use. We consider a discrete‐time version of GBS and introduce two new discrete‐time policies, labeled ADAPTIVE and PIPELINE. We prove the stochastic stability and finiteness of average inventory level under GBS, ADAPTIVE, and PIPELINE policies, in the important special case of bounded lead time. We use simulations to evaluate the performance of the three policies and their dependence on lead time distributions. We observe that the performance improvements, provided by our policies under practical constraints, can indeed be very significant, and they are larger when the lead time “randomness” (say, variance) is larger. It also appears that the PIPELINE policy typically has the best performance and is robust from the practical use point of view, in the sense that it applies to a wide range of practical scenarios and does not require careful parameter tuning.

  PublisherDOI

• An infinite server system with packing constraints and ranked servers

  Queueing Systems · 2025-06-22

  articleOpen access1st authorCorresponding

  Abstract A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $$1,2,3, \ldots $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> </mml:mrow> </mml:math> ; a server rank is its “location." Each customer has an independent exponentially distributed service time, with the mean determined by its type. Multiple customers (possibly of different types) can be placed for service into one server, subject to “packing” constraints. Service times of different customers are independent, even if served simultaneously by the same server. The large-scale asymptotic regime is considered, such that the mean number of customers r goes to infinity. We seek algorithms with the underlying objective of minimizing the location (rank) U of the right-most (highest ranked) occupied (non-empty) server. Therefore, this objective seeks to minimize the total number Q of occupied servers and keep the set of occupied servers as far at the “left” as possible, i.e., keep U close to Q . In previous work, versions of Greedy Random (GRAND) algorithm have been shown to asymptotically minimize Q / r as $$r\rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> . In this paper, we show that when these algorithms are combined with the First-Fit rule for “taking” empty servers, they asymptotically minimize U / r as well.

  PublisherOA PDFDOI

• A large-scale particle system with independent jumps and distributed synchronization

  Advances in Applied Probability · 2024-10-04 · 1 citations

  articleOpen accessSenior authorCorresponding

  Abstract We study a system consisting of n particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, and ‘synchronization’ jumps, which allow it to join a randomly chosen other particle if the latter happens to be ahead of it. The system state is the empirical distribution of particle locations. We consider the mean-field asymptotic regime where $n\to\infty$ . We prove that $v_n$ , the steady-state speed of advance of the particle system, converges, as $n\to\infty$ , to a limit $v_{**}$ which can easily be found from a minimum speed selection principle . Also we prove that as $n\to\infty$ , the system dynamics converges to that of a deterministic mean-field limit (MFL). We show that the average speed of advance of any MFL is lower-bounded by $v_{**}$ , and the speed of a ‘benchmark’ MFL, resulting from all particles initially being co-located, is equal to $v_{**}$ . In the special case of exponentially distributed independent jump sizes, we prove that a traveling-wave MFL with speed v exists if and only if $v\ge v_{**}$ , with $v_{**}$ having a simple explicit form; we also show the existence of traveling waves for the modified systems with a left or right boundary moving at a constant speed v . We provide bounds on an MFL’s average speed of advance, depending on the right tail exponent of its initial state. We conjecture that these results for exponential jump sizes extend to general jump sizes.

  PublisherOA PDFDOI

• Asymptotic optimality of dynamic first-fit packing on the half-axis

  arXiv (Cornell University) · 2024-04-04

  preprintOpen access

  We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and depart after an independent exponentially distributed unit mean service time. The arriving item sizes (lengths) are assumed to be independent and identically distributed (i.i.d.) from a common distribution $H$. A widely employed algorithm for allocating the items is the "first-fit" discipline, namely, each arriving item is placed in the left-most vacant interval large enough to accommodate it. In a seminal 1985 paper, Coffman, Kadota, and Shepp ([6]) proved that in the special case of unit length items (i.e. degenerate $H$), as $r$ tends towards infinity, the first-fit algorithm is asymptotically optimal in the following sense: the steady-state ratio of expected "empty space" (gaps between items) to expected occupied space tends towards $0$. In a sequel to [6], Coffman, Kadota, and Shepp ([5]) conjectured that the first-fit discipline is also asymptotically optimal for non-degenerate $H$. In this paper we provide the first proof of first-fit asymptotic optimality for non-degenerate distributions $H$ of item sizes. Our main result is for the case when $H$ is concentrated on countably many positive real sizes forming an increasing sequence that is either finite or goes to infinity, with the average item size being finite. We prove that under the first-fit discipline, as $r$ tends towards infinity, the steady-state packing configuration (scaled down by $r$) converges in distribution to the limiting packing configuration with smaller items on the left, larger items on the right, and with no gaps between. In particular, this proves asymptotic optimality of first-fit in the sense that in steady-state the empty space (scaled down by $r$) vanishes.

  PublisherOA PDFDOI

• An infinite server system with packing constraints and ranked servers

  arXiv (Cornell University) · 2024-07-01

  preprintOpen access1st authorCorresponding

  A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent exponentially distributed service time, with the mean determined by its type. Multiple customers (possibly of different types) can be placed for service into one server, subject to ``packing'' constraints. Service times of different customers are independent, even if served simultaneously by the same server. The large-scale asymptotic regime is considered, such that the mean number of customers $r$ goes to infinity. We seek algorithms with the underlying objective of minimizing the location (rank) $U$ of the right-most (highest ranked) occupied (non-empty) server. Therefore, this objective seeks to minimize the total number $Q$ of occupied servers {\em and} keep the set of occupied servers as far at the ``left'' as possible, i.e., keep $U$ close to $Q$. In previous work, versions of {\em Greedy Random} (GRAND) algorithm have been shown to asymptotically minimize $Q/r$ as $r\to\infty$. In this paper we show that when these algorithms are combined with the First-Fit rule for ``taking'' empty servers, they asymptotically minimize $U/r$ as well.

  PublisherOA PDFDOI

• Asymptotic Optimality of Constant-Order Policies in Joint Pricing and Inventory Models

  Mathematics of Operations Research · 2023-04-17 · 7 citations

  article

  We consider a classic joint pricing and inventory control problem with lead times, which is extensively studied in the literature but is notoriously difficult to solve because of the complex structure of the optimal policy. In this work, rather than analyzing the optimal policy, we propose a class of constant-order dynamic pricing policies, which are fundamentally different from base-stock list price policies, the primary emphasis in the existing literature. Under such a policy, a constant-order amount of new inventory is ordered every period, and a pricing decision is made based on the inventory level. The policy is independent of the lead time. We prove that the best constant-order dynamic pricing policy is asymptotically optimal as the lead time grows large, which is exactly the setting in which the problem becomes computationally intractable because of the curse of dimensionality. As our main methodological contributions, we establish the convergence to a long-run average random yield inventory model with zero lead time and ordering capacities by its discounted counterpart as the discount factor goes to one, nontrivially extending the previous results in Federgruen and Yang that analyze a similar model but without capacity constraints. Funding: Research of X. Chen and L. Xin was partly supported by the National Science Foundation [Grant CMMI-1635160].

  PublisherDOI

Frequent coauthors

• Cecelia Jankowski

  Institute of Electrical and Electronics Engineers

  412 shared

• Sequences Schwartz

  Institute of Electrical and Electronics Engineers

  412 shared

• James Jefferies

  Glasgow Royal Infirmary

  412 shared

• Sudhir R. Ghorpade

  412 shared

• Gregory W. Wornell

  412 shared

• Radu Bălan

  412 shared

• Kevin Lisankie

  Institute of Electrical and Electronics Engineers

  412 shared

• Prasad Narayana

  Rutgers, The State University of New Jersey

  412 shared

Education

• Ph.D., Industrial Engineering

  University of Illinois at Urbana-Champaign

  1990

• M.S., Industrial Engineering

  University of Illinois at Urbana-Champaign

  1986

• B.S., Industrial Engineering

  University of Illinois at Urbana-Champaign

  1984

Awards & honors

• INFORMS Fellow