arXiv subjects

Refael Hassin

Publications and source records attributed to Refael Hassin.

7 recordsLinked to original sources

arXiv2026

Using memory to control admission to unobservable queues

We study admission control to an unobservable M/M/1 queue. A memoryless controller can only randomly thin arrivals (random routing, RR). We show that a gated admission (GA) policy, blocking arrivals for a fixed period after each admission, stochastically dominates RR at equal throughput, improving social welfare under any sojourn-based cost. We characterize the welfare-maximizing threshold and define the Price of Forgetting as the welfare ratio. This ratio is unbounded even though the absolute welfare gain stays uniformly bounded.

math.PR↗

arXiv2022

Optimal and Self Selection of Service Type in a Queueing System where Long Service Postpones the Need for the Next Service

We study a make-to-order system with a finite set of customers. Production is stochastic with a nonlinear dependence between the ordered quantity and the production rate. Customers may have to queue until their turn arrives, and therefore their order decisions interact. Specifically, while being served, customers are aware of the queue length and choose one of two order quantities (or service types). The time to the next replenishment (their activity time) is stochastic and depends on the order quantities. A customer is inactive during service and while waiting in the queue. We refer to the type of service with a greater ratio of expected activity to service time as ``more efficient''. In the centralized case, the system is interested in maximizing the steady-state average number of active customers, which is referred to as the efficiency of the system. We show that choosing the more efficient service is not always optimal, but the optimal strategy can be approximated well by selecting one of three threshold strategies which depend on the number of inactive customers. In the decentralized case, each customer acts to maximize the fraction of time she is active. We observe that individuals and the manager have opposite incentives: When the queue is long, individuals tend to choose the long service, while the manager prefers the short service in this case. This makes the system difficult to regulate. However, we show that simply removing the less efficient service significantly increases efficiency.

math.OC↗

arXiv2019

How Advance Sales can Reduce Profits: When to Buy, When to Sell, and What Price to Charge

A consumer who wants to consume a good in a particular period may nevertheless attempt to buy it earlier if he is concerned that in delaying he would find the good already sold. This paper considers a model in which the good may be offered in two periods; the period in which all consumers most value the good (period 2), and an earlier period (period 1). Examining the profit-maximizing strategy of the firm under unbounded demand, we find that even with no cost of making the product available early, the firm does not profit, and usually loses, by making the product available early. Interestingly, the price that maximizes profits induces all arrivals to occur early, or all arrivals to occur late, depending on the parameters. The firm would not set a price which induces consumers to arrive in both periods. In particular, if the firm controls the penalty for arriving early, then it should set a high penalty so that no one arrives early. The Nash equilibrium behavior of consumers, when deciding if and when to arrive is more complicated than one may suppose, and can generate some unexpected behavior. For example, when there is unbounded demand, most potential consumers decide not to arrive at all. Additionally, the arrival rate may decline with the surplus a person gets from buying the good. Surprisingly, we find that an increase in the number of units for sale increases the number of consumers who arrive early. Moreover, we find that the profit-maximizing price increases with the number of units offered for sale. This too is unexpected as an increase in supply often results in price reduction. In our case, an increase in the number of units on sale also increases demand, and the seller may profit by increasing the price. In the single-unit case, we give closed solutions for the equilibrium customer behavior and profit-maximizing firm strategy and conduct sensitivity analysis.

econ.GN↗

arXiv2017

A strategic model of job arrivals to a single machine with earliness and tardiness penalties

We consider a game of decentralized timing of jobs to a single server (machine) with a penalty for deviation from a due date, and no delay costs. The jobs' sizes are homogeneous and deterministic. Each job belongs to a single decision maker, a customer, who aims to arrive at a time that minimizes his deviation penalty. If multiple customers arrive at the same time then their order of service is determined by a uniform random draw. We show that if the cost function has a weighted absolute deviation form then any Nash equilibrium is pure and symmetric, that is, all customers arrive together. Furthermore, we show that there exist multiple, in fact a continuum, of equilibrium arrival times, and provide necessary and sufficient conditions for the socially optimal arrival time to be an equilibrium. The base model is solved explicitly, but the prevalence of a pure symmetric equilibrium is shown to be robust to several relaxations of the assumptions: restricted server availability, inclusion of small waiting costs, stochastic job sizes, randomly sized population, heterogeneous due dates, and non-linear deviation penalties.

cs.GT↗

arXiv2016

On the price of anarchy in a single server queue with heterogenous service valuations induced by travel costs

This work presents a variation of Naor's strategic observable model (1969), by adding a component of customer heterogeneity induced by the location of customers in relation to the server. Accordingly, customers incur a travel cost which depends linearly on the distance of the customer from the server. The arrival of customers with distances less than x is assumed to be a Poisson process with rate lambda(x)=int_0^x h(y)dy<\infty, where h(y) is a nonnegative intensity function of the distance y. In a loss system M/G/1/1 we define the threshold Nash equilibrium strategy x_e and the optimal social threshold strategy x^*. We show that if the rate of arriving customers is bounded then PoA converges to 1 when x_e \to\infty, i.e., in the limit there is no difference between the social and equilibrium optimal benefits. The rest of the paper is dedicated for the case in which the rate of arriving customers is unbounded. We develop an explicit formula to calculate lim_{x_e\to \infty}PoA when it exists. We present sufficient conditions for the limit to exist and for the existence of a simple formula for calculating it. We prove that if the relation between two intensity functions converges to a positive constant, then the corresponding limits of PoA coincide. If, on the other hand, one intensity function is larger than the other from some point on, then under certain conditions the limit of PoA (if exists) will be larger for the larger intensity function. For all intensity functions h, we prove that if h converges to a constant then PoA converges to 2, and that if from some point on h decreases (increases) monotonically then the limit of PoA, if exists, is smaller (larger) than 2. In a system with a queue we prove that the price of anarchy may be unbounded already in the simple case of uniform arrival, namely h~c, where c>0.

math.OC↗

arXiv2016

Delay-minimizing capacity allocation in an infinite server queueing system

We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is an infinite sequence of service rates. We study the probabilistic properties of this system by considering overflows from sub-systems with a finite number of servers. Several stability measures are suggested and analysed. The tail of the series of service rates that minimizes the average expected delay (service time) is shown to be approximately geometrically decreasing. We use this property in order to approximate the optimal allocation of service rates by constructing an appropriate dynamic program.

math.PR↗

arXiv2011

Minimum diameter and cycle-diameter orientations on planar graphs

Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation H of G whose cycle diameter is bounded by a constant times the cycle diameter of G? We prove this property for planar graphs. These results have implications on the problem of approximating an orientation with minimum diameter

cs.DM↗