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17
Staffing of timevarying queues to achieve timestable performance
, 2005
"... Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probab ..."
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Cited by 28 (19 self)
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Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probability of delay. That procedure tends to produce timestable performance for several other operational measures. Motivated by telephone call centers, we focus on manyserver models with customer abandonment, especially the Markovian Mt/M/st + M model, having an exponential timetoabandon distribution (the +M), an exponential servicetime distribution and a nonhomogeneous Poisson arrival process. We develop three different methods for staffing, with decreasing generality and decreasing complexity: First, we develop a simulationbased iterativestaffing algorithm (ISA), and conduct experiments showing that it is effective. The ISA is appealing because it applies to very general models and is automatically validating: we directly see how well it works. Second, we extend the squarerootstaffing rule, proposed by Jennings et al., which is based on the associated infiniteserver model. The rule dictates that the staff level at time t be st = mt + β √ mt, where mt is the offered load (mean number of busy servers in the infiniteserver model) and the constant β reflects the service grade. We show that the service grade β in the staffing formula can be represented as a function of the target delay probability α by
Locating Mobile Nodes with EASE: Learning Efficient Routes from Encounter Histories Alone
 IEEE/ACM Trans. Netw
, 2006
"... Abstract — Routing in largescale mobile ad hoc networks is challenging because all the nodes are potentially moving. Geographic routing can partially alleviate this problem, as nodes can make local routing decisions based solely on the destinations ’ geographic coordinates. However, geographic rout ..."
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Cited by 20 (3 self)
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Abstract — Routing in largescale mobile ad hoc networks is challenging because all the nodes are potentially moving. Geographic routing can partially alleviate this problem, as nodes can make local routing decisions based solely on the destinations ’ geographic coordinates. However, geographic routing still requires an efficient location service, i.e., a distributed database recording the location of every destination node. Devising efficient, scalable, and robust location services has received considerable attention in recent years. The main purpose of this paper is to show that node mobility can be exploited to disseminate destination location information without incurring any communication overhead. We achieve this by letting each node maintain a local database of the time and location of its last encounter with every other node in the network. This database is consulted by packets to obtain estimates of their destination’s current location. As a packet travels towards its destination, it is able to successively refine an estimate of the destination’s precise location, because node mobility has “diffused ” estimates of that location. We define and analyze a very simple algorithm called EASE (Exponential Age Search) and show that in a model where Θ(n) nodes perform independent random walks on a square lattice of size n, the length of the routes computed by EASE are of the same order as the distance between the source and destination even for very large n. Therefore, without disseminating any explicit location information, the length of EASE routes are within a constant factor of routes obtained with perfect information. We discuss refinements of the EASE algorithm and evaluate it through extensive simulations. We discuss general conditions such that the mobility diffusion effect leads to efficient routes without an explicit location service. In practical settings, where these conditions may not always be met, we believe that the mobility diffusion effect can complement existing location services and enhance their robustness and scalability. Index Terms — Mobile wireless networks, mobility, location service, routing. I.
Extreme nash equilibria
 In Proc. of the 8th Italian Conference on Theoretical Computer Science, LNCS 2841
, 2003
"... Abstract. We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a ..."
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Cited by 20 (10 self)
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Abstract. We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel links, to control the routing of its own assigned traffic. InaNash equilibrium, each user routes its traffic on links that minimize its expected latency cost. Our structural results provide substantial evidence for the Fully Mixed Nash Equilibrium Conjecture, which states that the worst Nash equilibrium is the fully mixed Nash equilibrium, where each user chooses each link with positive probability. Specifically, we prove that the Fully Mixed Nash Equilibrium Conjecture is valid for pure Nash equilibria and that under a certain condition, the social cost of any Nash equilibrium is within a factor of 6 + ε, of that of the fully mixed Nash equilibrium, assuming that link capacities are identical.
ModelBased Design Exploration of Wireless Sensor Node Lifetimes
 In European conference on Wireless Sensor Networks (EWSN) 07
, 2007
"... Abstract. This paper presents two lifetime models that describe two of the most common modes of operation of sensor nodes today, triggerdriven and dutycycle driven. The models use a set of hardware parameters such as power consumption per task, state transition overheads, and communication cost to ..."
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Cited by 9 (1 self)
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Abstract. This paper presents two lifetime models that describe two of the most common modes of operation of sensor nodes today, triggerdriven and dutycycle driven. The models use a set of hardware parameters such as power consumption per task, state transition overheads, and communication cost to compute a node’s average lifetime for a given event arrival rate. Through comparison of the two models and a case study from a real camera sensor node design we show how the models can be applied to drive architectural decisions, compute energy budgets and dutycycles, and to preform sidebyside comparison of different platforms. 1
Sensor Node Lifetime Analysis: Models and Tools
"... This paper presents two lifetime models that describe two of the most common modes of operation of sensor nodes today, triggerdriven and dutycycle driven. The models use a set of hardware parameters such as power consumption per task, state transition overheads, and communication cost to compute a ..."
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Cited by 8 (0 self)
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This paper presents two lifetime models that describe two of the most common modes of operation of sensor nodes today, triggerdriven and dutycycle driven. The models use a set of hardware parameters such as power consumption per task, state transition overheads, and communication cost to compute a node’s average lifetime for a given event arrival rate. Through comparison of the two models and a case study from a real camera sensor node design we show how the models can be applied to drive architectural decisions, compute energy budgets and dutycycles, and to preform sidebyside comparison of different platforms. Based on our models we present a MATLAB Wireless Sensor Node Platform Lifetime Prediction & Simulation Package (MATSNL). This demonstrates the use of the models using sample applications drawn from existing sensor node measurements.
Realtime delay estimation based on delay history
, 2007
"... Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the ..."
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Cited by 8 (4 self)
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Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative realtime delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delayhistory estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multiserver queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the manyserver and classical heavytraffic limiting regimes.
An asymptotically efficient simulationbased algorithm for finite horizon stochastic dynamic programming
 IEEE Trans. on Automatic Control
, 2007
"... Abstract — We present a simulationbased algorithm called “Simulated Annealing Multiplicative Weights ” (SAMW) for solving large finitehorizon stochastic dynamic programming problems. At each iteration of the algorithm, a probability distribution over candidate policies is updated by a simple multip ..."
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Cited by 6 (3 self)
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Abstract — We present a simulationbased algorithm called “Simulated Annealing Multiplicative Weights ” (SAMW) for solving large finitehorizon stochastic dynamic programming problems. At each iteration of the algorithm, a probability distribution over candidate policies is updated by a simple multiplicative weight rule, and with proper annealing of a control parameter, the generated sequence of distributions converges to a distribution concentrated only on the best policies. The algorithm is “asymptotically efficient, ” in the sense that for the goal of estimating the value of an optimal policy, a provably convergent finitetime upper bound for the sample mean is obtained. Index Terms — stochastic dynamic programming, Markov decision processes, simulation, learning algorithms, simulated annealing I.
The impact of increased employee retention upon performance in a customer contact center
 Manufacturing and Service Operations Management
"... A mathematical model is developed to help analyze the benefit in contactcenter performance obtained from increasing employee (agent) retention, by increasing agent job satisfaction. The contactcenter “performance ” may be restricted to a traditional productivity measure such as the number of cal ..."
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Cited by 6 (2 self)
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A mathematical model is developed to help analyze the benefit in contactcenter performance obtained from increasing employee (agent) retention, by increasing agent job satisfaction. The contactcenter “performance ” may be restricted to a traditional productivity measure such as the number of calls answered per hour or it may include a broader measure of the quality of service, e.g., revenue earned per hour or the number of problems successfully resolved per hour. The analysis is based on an idealized model of a contact center, in which the number of employed agents is constant over time, assuming that a new agent is immediately hired to replace each departing agent. The agent employment periods are assumed to be independent and identically distributed random variables with a general agentretention probability distribution, which depends upon management policy and actions. The steadystate staffexperience distribution is obtained from the agentretention distribution by applying renewal theory. An increasing realvalued function specifies the average performance as a function of agent experience. Convenient closedform expressions for the overall performance as a function of model elements are derived when either the agentretention distribution or the performance function has exponential structure. Management actions may cause the agentretention distribution to change. The model describes the consequences of such changes upon the longrun average staff experience and the longrun average performance.
Maximizing the Throughput of Tandem Lines with Flexible FailureProne Servers and Finite Buffers
, 2007
"... Consider a tandem queueing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stat ..."
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Cited by 4 (3 self)
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Consider a tandem queueing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stations with the goal of maximizing the longrun average throughput. Our main conclusion is that the presence of server failures does not have a major impact on the optimal assignment of servers to stations for the systems we consider. More specifically, we show that when the servers are generalists, any nonidling policy is optimal, irrespective of the reliability of the servers. We also provide theoretical and numerical results for Markovian systems with two stations and two or three servers that suggest that the structure of the optimal server assignment policy does not depend on the reliability of the servers, and that ignoring server failures when assigning servers to stations yields nearoptimal throughput. Finally, we present numerical results that illustrate that simple server assignment heuristics designed for larger systems with reliable servers also yield good throughput performance in Markovian systems with three stations and three failureprone servers.
2008): "Age, Luck and Inheritance
 NBER Working Paper
"... We introduce the investment risk into a heterogeneous agents model and present a mechanism to analytically generate a double Pareto distribution of wealth. We replicate the distribution of the U.S. wealth and especially the three prominent features: a high Gini coe ¢ cient, skewness to the right, an ..."
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Cited by 3 (3 self)
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We introduce the investment risk into a heterogeneous agents model and present a mechanism to analytically generate a double Pareto distribution of wealth. We replicate the distribution of the U.S. wealth and especially the three prominent features: a high Gini coe ¢ cient, skewness to the right, and Pareto tails. We disentangle the contribution of inheritance, age and stochastic rates of capital return to wealth inequality, in particular to the Gini coe ¢ cient. Finally, we investigate the e¤ects of the …scal and redistributive policies on wealth inequality and social welfare.