Priority Auctions and Queue Disciplines that Depend on Processing Time

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium

Advance reservations and information sharing in queues with strategic customers

In many branches of the economy, including transportation, lodging, and more recently cloud computing, users can reserve resources in advance. Although advance reservations are gaining popularity, little is known about the strategic behavior of customers facing the decision whether to reserve a resource in advance or not. Making an advance reservation can reduce the waiting time or the probability of not getting service, but it is usually associated with an additional cost. To evaluate this trade-off, we develop a game-theoretic framework, called advance reservation games, that helps in reasoning about the strategic behavior of customers in systems that allow advance reservations. Using this framework, we analyze several advance reservation models, in the context of slotted loss queues and waiting queues. The analysis of the economic equilibria, from the provider perspective, yields several key insights, including: (i) If customers have no a-priori information about the availability of servers, then only customers granted service should be charged a reservation fee; (ii) Informing customers about the exact number of available servers is less profitable than only informing them that servers are available; (iii) In many cases, the reservation fee that leads to the equilibrium with maximum possible profit leads to other equilibria, including one resulting with no profit; (iv) If the game repeats many times and customers update their strategy after observing actions of other customers at previous stage, then the system converges to an equilibrium where no one makes an advance reservation, if such an equilibrium exists. Else, the system cycles and yields positive profit to the provider Finally, we study the impact of information sharing in M/M/1 queues with strategic customers. We analyze the intuitive policy of sharing the queue length with customers when it is small and hiding it when it is large. We prove that, from the provider perspective, such a policy is never optimal. That is, either always sharing the queue length or always hiding it maximizes the average number of customers joining the queue

System Dynamics Simulation to Test Operational Policies in the Milk-Cheese Supply Chain Case study: Piar Municipality, Bolivar State, Venezuela.

With the purpose of detecting the impact that variations of demand cause in the milk-cheese supply chain, and determining how the operational policies of capacity, inventories or labor force can mitigate this impact, a system dynamics simulation model has been designed based on a survey conducted on a sample of cheese manufacturers and their links with milk farms, transportation companies and cheese distributors. This supply chain will be consolidated when a milk center that will collect the raw milk is completed. From this center, and after adequate treatment, milk will be distributed to the different cheese manufacturers in the supply chain. Managing adequately the milk-cheese supply chain represents an important challenge due to the short life of these products. Although this study was done in a region in Latin America, its results can be applicable to food supply chains by introducing some modifications. The milk-cheese supply chain in this case study contemplates three milk producers, one milk center, five cheese producers and several distributing agents. These companies operate individually under normal conditions, but they have understood that their integration in a supply chain improves the competitiveness of all its members. That is to say, the sum is greater than the parts. For its initial design a simulation software model is used in which the resources of the supply chain are optimized. Later the product of this optimization facilitates some initial values to be used in the system dynamics model in which causeeffect or influence relationships have been previously established considering the most representative variables. Finally, changes in operational policies that can reduce the level of pending orders in the supply chain are tested using other simulation software. The main contribution of this research is that it can serve as support or contribute to reduce the uncertainty in the decision making process of the supply chain management due to the speed with which individual or combined policies can be analyzed. In response to a variation of demand the most adequate policy may be selected and that can be done before the policy is implemented

Equilibrium and Learning in Queues with Advance Reservations

Consider a multi-class preemptive-resume $M/D/1$ queueing system that supports advance reservations (AR). In this system, strategic customers must decide whether to reserve a server in advance (thereby gaining higher priority) or avoid AR. Reserving a server in advance bears a cost. In this paper, we conduct a game-theoretic analysis of this system, characterizing the equilibrium strategies. Specifically, we show that the game has two types of equilibria. In one type, none of the customers makes reservation. In the other type, only customers that realize early enough that they will need service make reservations. We show that the types and number of equilibria depend on the parameters of the queue and on the reservation cost. Specifically, we prove that the equilibrium is unique if the server utilization is below 1/2. Otherwise, there may be multiple equilibria depending on the reservation cost. Next, we assume that the reservation cost is a fee set by the provider. In that case, we show that the revenue maximizing fee leads to a unique equilibrium if the utilization is below 2/3, but multiple equilibria if the utilization exceeds 2/3. Finally, we study a dynamic version of the game, where users learn and adapt their strategies based on observations of past actions or strategies of other users. Depending on the type of learning (i.e., action learning vs.\ strategy learning), we show that the game converges to an equilibrium in some cases, while it cycles in other cases

A First Approach on Modelling Staff Proactiveness in Retail Simulation Models

There has been a noticeable shift in the relative composition of the industry in the developed countries in recent years; manufacturing is decreasing while the service sector is becoming more important. However, currently most simulation models for investigating service systems are still built in the same way as manufacturing simulation models, using a process-oriented world view, i.e. they model the flow of passive entities through a system. These kinds of models allow studying aspects of operational management but are not well suited for studying the dynamics that appear in service systems due to human behaviour. For these kinds of studies we require tools that allow modelling the system and entities using an object-oriented world view, where intelligent objects serve as abstract \'actors\' that are goal directed and can behave proactively. In our work we combine process-oriented discrete event simulation modelling and object-oriented agent based simulation modelling to investigate the impact of people management practices on retail productivity. In this paper, we reveal in a series of experiments what impact considering proactivity can have on the output accuracy of simulation models of human centric systems. The model and data we use for this investigation are based on a case study in a UK department store. We show that considering proactivity positively influences the validity of these kinds of models and therefore allows analysts to make better recommendations regarding strategies to apply people management practices.Retail Performance, Management Practices, Proactive Behaviour, Service Experience, Agent-Based Modelling, Simulation