Gideon Weiss

• University of Haifa

We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idlin...

We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idlin...

The N-System with independent Poisson arrivals and exponential server-dependent service times under first come first served and assign to longest idle server policy has explicit steady state distribution. We scale the arrival and the number of servers simultaneously, and obtain the fluid and central limit approximation for the steady state. This is...

We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idlin...

We consider continuous linear programs over a continuous finite time horizon T, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear progr...

We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear pro...

We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer service times. The static planning linear programming approach (Harrison and Lopez \cite{harrison-lopez:99}) is use...

We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer service times. The static planning linear programming approach (Harrison and Lopez \cite{harrison-lopez:99}) is use...

We study a parallel service queueing system with servers of types $s_1,\ldots,s_J$, customers of types $c_1,\ldots,c_I$, bipartite compatibility graph $\mathcal{G}$, where arc $(c_i, s_j)$ indicates that server type $s_j$ can serve customer type $c_i$, and service policy of first come first served FCFS, assign longest idle server ALIS. For a genera...

We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on...

We prove two lemmas with conditions that a system, which is described by a transient Markov chain, will display local stability. Examples of such systems include partly overloaded Jackson networks, partly overloaded polling systems, and overloaded multi-server queues with skill based service, under first come first served policy.

The model of FCFS infinite bipartite matching was introduced in caldentey-kaplan-weiss 2009. In this model there is a sequence of items that are chosen i.i.d. from $\mathcal{C}=\{c_1,\ldots,c_I\}$ and an independent sequence of items that are chosen i.i.d. from $\mathcal{S}=\{s_1,\ldots,s_J\}$, and a bipartite compatibility graph $G$ between $\math...

We consider a queueing system with servers S={m1,...,mJ}, and with customer types C={a,b,...}. A bipartite graph G describes which pairs of server-customer types are compatible. We consider FCFS-ALIS policy: A server always picks the first, longest waiting compatible customer, and a customer is always assigned to the longest idle compatible server....

We consider a queueing system with J parallel servers [Formula: see text], and with customer types 𝒞 = {a, b, …}. A bipartite graph G describes which pairs of server-customer types are compatible. We consider FCFS-ALIS policy: A server always picks the first, longest waiting compatible customer, and a customer is always assigned to the longest idle...

We consider continuous linear programs over continuous time finite horizon $T$, with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, together with their symmetric dual. We search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the...

We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Towar...

We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the Separated Continuous Linear...

In the era of multicore and manycore processors, a systematic engineering approach for software performance becomes more and more crucial to the success of modern software systems. This article argues for more software performance engineering research ...

We propose an estimator for the cumulative distribution function G of the sojourn time in a steady-state M/G/∞ queueing system, when the available data consists of the arrival and departure epochs alone, without knowing which arrival corresponds to which departure. The estimator generalizes an estimator proposed in Brown (1970), and is based on a f...

We study an overloaded service system with servers of types S={s1,…,sJ}S={s1,…,sJ}, serving customers of types C={c1,…,cI}C={c1,…,cI} under FCFS. Customers arrive in Poisson streams, join the queue and then abandon or get served. Service is skill based, which is described by a compatibility graph GG, where (i,j)∈G(i,j)∈G if server type sjsj is trai...

We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m i can serve a subset of job types \(\mathcal{C}(m_{i})\). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find se...

Motivated by queues with multi-type servers and multi-type customers, we consider an infinite sequence of items of types C = {c1, . . . , cI }, and another infinite sequence of items of types S = {s1, . . . , sJ }, and a bipartite graph G of allowable matches between the types. We assume that the types of items in the two sequences are i.i.d. with...

We consider a memoryless loss system with servers = {1, …, J}, and with customer types = {1, …, I}. Servers are multi-type: server j works at rate μj, and can serve a subset of customer types C(j). An arriving customer will go to the longest idling server which can serve him, or be lost. We obtain a simple explicit steady-state distribution for thi...

We consider large volume job shop scheduling problems, in which there is a fixed number of machines, a bounded number of activities per job, and a large number of jobs. In large volume job shops it makes sense to solve a fluid problem and to schedule the jobs in such a way as to track the fluid solution. There have been several papers which used th...

We consider a memoryless Erlang loss system with servers = {1, …, J}, and with customer types = {1, …, I}. Servers are multitype, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reve...

We consider a push pull queueing system with two servers and two types of jobs which are processed by the two servers in opposite order, with stochastic generally distributed pro- cessing times. This push pull system was introduced by Kop- zon and Weiss, who assumed exponential processing times. It is similar to the Kumar-Seidman Rybko-Stolyar (KSR...

We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant...

We consider an infinite sequence of customers of types C = {1, 2, ..., I} and an infinite sequence of servers of types s = {1, 2, ... J}, where a server of type j can serve a subset of customer types C(j) and where a customer of type i can be served by a subset of server types S(i). We assume that the types of customers and servers in the infinite...

We consider an infinite sequence of customers of types and an infinite sequence of servers of types where a server of type j can serve a subset of customer types C(j) and where a customer of type i can be served by a subset of server types S(i). We assume that the types of customers and servers in the infinite sequences are random, independent, and...

We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between...

We consider the separated continuous linear programming problem with linear data. We characterize the form of its optimal solution, and present an algorithm which solves it in a finite number of steps, using an analog of the simplex method, in the space of bounded measurable functions.

We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form λ *+∑v i where λ * is the rate of outputs and v i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in ma...

Peer-to-peer (P2P) overlay networks such as BitTorrent and Avalanche are increasingly used for disseminating potentially large files from a server to many end users via the Internet. The key idea is to divide the file into many equally-sized parts and then let users download each part (or, for network coding based systems such as Avalanche, linear...

In recent years, overlay networks have proven a popular way of disseminating potentially large files from a single server S to a potentially large group of N end users via the Internet. A number of algorithms and protocols have been suggested, implemented and studied. In particular, much attention has been given to peer-to-peer (P2P) systems such a...

We consider a two machine 3 step re-entrant line, with an infinite supply of work. The service discipline is last buffer first served. Processing times are independent exponentially distributed. We analyze this system, obtaining steady state behavior and sample path properties.

In recent years, overlay networks have proven an effective way of disseminating a file from a single source to a group of end users via the Internet. A number of algorithms and protocols have been suggested, implemented and studied. In particular, much attention has been given to peer-to-peer (P2P) systems such as BitTorrent, Slurpie, SplitStream a...

Peer-to-peer (P2P) overlay networks such as BitTorrent and Avalanche are increasingly used for disseminating potentially large files from a server to many end users via the Internet. The key idea is to divide the file into many equally-sized parts and then let users download each part (or, for network coding based systems such as Avalanche, linear...

We consider systems in which many items are evolving over time by sharing common resources, and the problem of how to control such systems by allocating resources to various activities which schedule, route and process these items. We represent this by a processing network as defined by Harrison, with the added feature of infinite virtual buffers,...

We consider a Jackson network in which some of the nodes have an infinite supply of work: when all the customers queued at such a node have departed, the node will process a customer from this supply. Such nodes will be processing jobs all the time, so they will be fully utilized and experience a traffic intensity of 1. We calculate flow rates for...

We consider a Jackson network in which some of the nodes have an infinite supply of work: when all the customers queued at such a node have departed, the node will process a customer from this supply. Such nodes will be processing jobs all the time, so they will be fully utilized and experience a traffic intensity of 1. We calculate flow rates for...

We consider a two machine 3 step re-entrant line, with an infinite supplyof work. We assume that processing times are exponentiallydistributed. We show that this system is stable under LBFS priority policy.

We consider a Jackson network with two nodes, with no exogenous input, but instead an infinite supply of work at each of the nodes: whenever a node is empty, it processes a job from this infinite supply. We obtain an explicit expression for the steady state distribution of this system, as an infinite sum of product forms.

We consider a two machine 3 step re-entrant line, with an infinite supply of work. We assume that processing times are exponentially distributed. We show that this system is stable under LBFS priority policy.

We consider a two node multiclass queueing network given by two machines each with two classes. There are two streams of jobs. One stream originates in machine 1, which feeds it for further processing to machine 2, and the other stream moves in the opposite direction. We describe a policy for this system which is stable and which keeps both machine...

We describe a simple on-line heuristic for scheduling job-shops. We assume there is a fixed set of routes for the jobs, and many jobs on each route. The heuristic uses safety stocks to keep the bottleneck machine busy, while the other machines keep time with it. We perform a probabilistic analysis of the heuristic, and obtain probabilistic bounds o...

We consider the following job-shop scheduling problem: N jobs move through I machines, along R routes, with given processing times, and one seeks a schedule to minimize the latest job completion time. This problem is NP-hard. We are interested in the case where the number of routes and the number of machines are fixed, while the number of jobs vari...

We consider the increasing sequence of non-intersecting monotone decreasing RCLL step processes Y ∗ n (t) ,n =1 , 2 ,... ( t> 0) whose jump points cover all the points of the homogeneous rate 1 Poisson process on the quadrant R2 +. We derive properties of these processes, in particular the marginal distributions IP(Y ∗ n (t) >x ), in terms of a Toe...

We survey four proofs that the Gittins index priority rule is optimal for alternative bandit processes. These include Gittins' original exchange argument, Weber's prevailing charge argument, Whittle's Lagrangian dual approach, and a proof based on generalized conservation laws and LP duality.

We consider a process that starts at height y, stays there for a time X0 [similar] exp(y) when it drops to a level Z1 [similar] U(0, y). Thereafter it stays at level Zn for time Xn [similar] exp(Zn), then drops to a level Zn+1 [similar] U(0,Zn). We investigate properties of this process, as well as the Poisson hyperbolic process which is o...

In a fluid re-entrant line, fluid moves through a sequence of K buffers, partitioned by their service to I stations. We consider theinitial fluid in the system, with no external input.Our objective is to empty all the fluid in the line with minimum total inventory. We presenta polynomial time algorithm for this problem, for the case I = 2.

This paper studies the uid approximation, also known as the functional strong law-of-large-numbers, for a GI/G/1 queue under a processor-sharing service discipline. The uid (approximation) limit in general depends on the service time distribution, and the convergence is in general in the Skorohod J 1 topology. This is in contrast to the known resul...

We study a 2-machine flowshop in which all processing times are inde- pendently and identically distributed, with values known to the scheduler. We are able to describe in detail the expected behavior of the flowshop under optimal and under heuristic schedules. Our results suggest that minimizing makespan might be a superfluous objective: Schedulin...

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the...

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the...

Recent results have shown a close connection between stability of stochastic networks and stability of their fluid models. A converse to the problem of stability is the question of optimal control of such networks. This motivates our search for optimal control of fluid models. We consider re-entrant lines in which parts move in a fixed route that m...

Customers move through a series of M service stations. Each customer, independent of all others, requires service from only one of the stations, for a duration of 1 time unit, this being station i with probability p i . The customer has zero service at all the other stations, but there is no overtaking between the customers, and so queueing occurs....

In this paper we extend previous results (by Browne and Yechiali) on dynamic priority rules in polling systems to a new version of a polling system where a number of servers c are coupled together as they service the stations. Index rules are derived to optimize system performance.

Consider scheduling a batch of jobs with stochastic processing times on parallel machines, with minimization of expected weighted flowtime as objective. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time, provides a natural heuristic for this problem. In a previous paper we have found an upper bound for...

We analyze the optimal preemptive sequencing of n jobs on M + 1 parallel identical machines to minimize expected total flowtime. The running times of the jobs are independent samples from the distribution Pr(X = H) = p, Pr(X = H + T) = 1 − p, where H, T are random variables of general distribution. Preemption of a job is allowed when H is completed...

We study the optimality of expected earliest due date sequencing of n jobs on M parallel identical machines, to minimize the total tardiness. The processing times of the jobs are assumed to be identically distributed with distribution function F(x), and the due date of job j, D j , j=1,⋯,n is assumed to be distributed with distribution function G j...

We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.

We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We...

We consider M machines in tandem with an infinite supply of jobs and no intermediate storage, and look for the order of the machines which will maximize the throughput. We show that if processing times on the machines are comparable in the sense of likelihood ratio, then it is optimal to use slower machines in the first and last position than in th...

We investigate the optimal allocation of effort to a collection of n projects. The projects are 'restless' in that the state of a project evolves in time, whether or not it is allocated effort. The evolution of the state of each project follows a Markov rule, but transitions and rewards depend on whether or not the project receives effort. The obje...

We investigate the optimal allocation of effort to a collection of n projects. The projects are ‘restless' in that the state of a project evolves in time, whether or not it is allocated effort. The evolution of the state of each project follows a Markov rule, but transitions and rewards depend on whether or not the project receives effort. The obje...

A set of ni arms of type i, i = 1,…, L, is available. A pull of arm of type i occupies a duration Vi at the end of which a reward Ci and Ni1,…, NiL new arms are obtained, while all other arms are frozen. A Gittins priority order of types is obtained and shown to yield the maximal discounted reward from this branching process of arms.

The minimum spillage sequencing problem, which arises in real-time satellite signal data processing, requires a set of numbers to be arranged so as to minimize the "overflow" of the partial sums above an upper bound. We subject several heuristics to worst-case analysis, average-case analysis, and computational testing. The results demonstrate that...

We consider a situation in which n jobs, requiring random amounts of processing, all with the same mean, are to be scheduled on m parallel machines with respect to one of two objectives: expected flowtime and expected makespan. We discuss optimality of the rule that says to schedule the jobs with the largest variance first (LVF). We show that for s...

In many classical combinatorial optimization problems, including critical and shortest paths, maximum flow, and network reliability, the introduction of uncertainty considerably complicates the calculation of system performance. In fact, in these contexts, computing system performance exactly can often be an impossible task. Therefore, obtaining st...

We consider n jobs with independent exponentially distributed processing times that are to be processed on two machines operating in parallel. The jobs are subject to precedence constraints that have the form of an intree, i.e., each job, except for the last one, has one direct successor. A job is at level l if its successor is at level l-1 the las...

A set of n spare components whose life lengths are exponentially distributed with rates μ1, …,μn are available to keep a two-component parallel system in operation. We derive the optimal order of replacement of failed components in order to maximize the system life length.

We consider the problem of minimizing the expected makespan of n jobs with independent exponentially distributed processing times on two parallel machines, under resource constraints. Job j has expected processing time 1/\mu _j and requires throughout its processing an amount r_j of a resource; the total amount of resource avail...

In various network models the quantities of interest are optimal value functions of the form max X i , min X i , min maxX i , max minX i , where the inner operation is on the nodes of a path/cut and the outer operation on all paths/cuts, e.g. shortest path of a project network, maximal flow of a flow network or lifetime of a reliability system....

In a graphical procedure for comparing k treatment means in a one-way ANOVA, one displays uncertainty intervals around the sample means and judges any pair to be significantly different if and only if their uncertainty intervals do not overlap. A graphical procedure is a Multiple Comparison Procedure (MCP) if and only if it controls the experimentw...

m Parallel machines are available for the processing of n jobs. The jobs require random amounts of processing. When processing times are exponentially distributed, SEPT (shortest expected processing time first) minimizes the flowtime, LEPT (longest expected processing time first) minimizes the makespan and maximizes the time to first machine idlene...

We consider an r-player version of the famous problem of the points, which was the stimulus for the correspondence between Pascal and Fermat in the 17th century. At each play of a game, exactly one of the players wins a point, player i winning with probability pi. The game ends the first time a player has accumulated his or her required number of p...

We consider a system that is composed of finitely many independent components each of which is either “on” or “off” at any time. The components are initially on and they have common on-time distributions. Once a component goes off, it remains off forever. The system is monotone in the sense that if the system is off whenever each component in a sub...

We consider preemptive scheduling of N tasks on m processors; processors have different speeds, tasks require amounts of work which are exponentially distributed, with different parameters. The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor avail...

We consider preemptive scheduling of N tasks on m processors; processors have different speeds, tasks require amounts of work which are exponentially distributed, with different parameters. The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor avail...

We consider the problem of scheduling n tasks on two identical parallel processors. We show both in the case when the processing times for the n tasks are independent exponential random variables, and when they are independent hyperexponentials which are mixtures of two fixed exponentials, that the policy of performing tasks with longest expected p...

A single server facility is equipped to perform a collection of operations. The service rendered to a customer is a branching process of operations. While the performance of an operation may not be interrupted before its completion, once completed, the required follow-up work may be delayed, at a cost per unit time of waiting that depends on the ty...

A shot noise process consisting of a series of events at random times and of random magnitudes, each of which produces a fixed shaped rise and recession, is used as the basis for describing continuous time streamflows. This type of model is chosen for its ability to model recessions. Recession shapes consisting of one or two exponential curves are...

Time-reversibility is defined for a process X(t) as the property that left brace X(t//1),. . . , X(t//n) right brace and left brace X( minus t//1),. . . , X( minus t//n) right brace have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian proces...

Time-reversibility is defined for a process X(t) as the property that {X(t1), …, X(tn )} and {X(– t1), …, X(– tn )} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.

We suggest a fluid framework for solving scheduling and control problems of manufacturing systems. We formulate the fluid approximation, show how to solve it, give an important graphical display of the fluid solution, construct a schedule from the fluid solution, and provide probabilistic bound of its suboptimality.

Issued as Reports [nos. 1-16], Project no. E-24-603