### oro.open.ac.uk Enhanced Cell Visiting Probability for QoS Provisioning in Mobile Multimedia Communications

, 2004

"... and other research outputs Enhanced cell visiting probability for QoS provisioning in mobile multimedia communications ..."

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and other research outputs Enhanced cell visiting probability for QoS provisioning in mobile multimedia communications

### Revenue and Capacity Management for a Multi-class Service System∗

, 2008

"... We consider the revenue and capacity management for a multi-class service system. Customer arrival rate for each class is price dependent. Admitted customers leave the system at constant class-dependent rates. Customers are rejected when the system is full. We start with a infinite-horizon dynamic p ..."

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We consider the revenue and capacity management for a multi-class service system. Customer arrival rate for each class is price dependent. Admitted customers leave the system at constant class-dependent rates. Customers are rejected when the system is full. We start with a infinite-horizon dynamic programming formulation and study the properties of the optimal control policy. Furthermore, we consider a fluid model which is formulated as an infinite horizon optimal control problem with a state space constraint where the objective is to maximize total discounted revenue. We analyze the dynamic pricing policy in the context of the fluid model and characterize its optimal solution. Solution of the fluid model is used to construct a capacity management model where the decision is the total system capacity level. The fluid model can be viewed as a deterministic fluid approximation of a stochastic service system. Throughout, we consider an admission control problem where the prices are fixed and customer service requests are either accepted or rejected upon arrival as a special case. 1

### Applied Probability Trust (19 November 2004) DYNAMIC ADMISSION CONTROL FOR LOSS SYSTEMS WITH BATCH ARRIVALS

"... We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches, where each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of “preferred class ” for ..."

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We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches, where each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of “preferred class ” for systems receiving mixed and one-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

### Optimal Policies for Control of Peers in Online Multimedia Services

"... Abstract — In this paper we consider a distributed peer-based system with a centralized controller responsible for managing the peers. For this system customers request large volumes of information such as video clips which instead of retrieving from a centralized repository of a parent organization ..."

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Abstract — In this paper we consider a distributed peer-based system with a centralized controller responsible for managing the peers. For this system customers request large volumes of information such as video clips which instead of retrieving from a centralized repository of a parent organization are obtained from peers that possess the clips. Peers act as servers only for a short duration and therefore the parent organization (i.e. centralized controller) would need to add new peer servers from time to time. This centralized “admission ” control of deciding whether or not to admit a customer with a video clip as a peer based on the system state (number of waiting requests and number of existing peers) is the crux of this research. The problem can be posed as a discrete stochastic optimal control and is formulated using a Markov decision process approach with infinite horizon and discounted cost/reward. We show that a stationary threshold policy in terms of the state of the system is optimal. In other words the optimal decision whether or not to accept a customer as a peer server is characterized by a switching curve. In typical Markov decision processes, it is extremely difficult to derive an analytical expression for the switching curve. However, using an asymptotic analysis, by suitably scaling time and states taking fluid limits, we show how this can be done for our problem. In addition, the asymptotic analysis can also be used to show that the switching curve is independent of the model parameters such as customer arrival rate, downloading times and peer-server lifetimes. Several numerical results are presented to support the analytical claims based on asymptotic analysis. I.

### ©2005 INFORMS Capacity Management in Rental Businesses with Two Customer Bases

"... We consider the allocation of capacity in a system in which rental equipment is accessed by two classes of customers. We formulate the problem as a continuous-time analogue of the one-shot allocation problems found in the more tradi-tional literature on revenue management, and we analyze a queueing ..."

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We consider the allocation of capacity in a system in which rental equipment is accessed by two classes of customers. We formulate the problem as a continuous-time analogue of the one-shot allocation problems found in the more tradi-tional literature on revenue management, and we analyze a queueing control model that approximates its dynamics. Our investigation yields three sets of results. First, we use dynamic programming to characterize properties of optimal capacity allocation policies. We identify conditions under which “complete sharing”—in which both classes of customers have unlimited access to the rental fleet—is optimal. Next, we develop a computationally efficient “aggregate threshold ” heuristic that is based on a fluid approximation of the original stochastic model. We obtain closed-form expressions for the heuristic’s control parameters and show that the heuristic performs well in numerical experiments. The closed-form expressions also show that, in the context of the fluid approximation, revenues are concave and increasing in the fleet size. Finally, we consider the effect of the ability to allocate capacity on optimal fleet size. We show that the optimal fleet size under allocation policies may be lower, the same as, or higher than that under complete sharing. As capacity costs increase, allocation policies allow for larger relative fleet sizes. Numerical results show that, even in cases in which dollar profits under complete sharing may be close to those under allocation policies, the capacity reductions enabled by allocation

### Applied Probability Trust (9 January 2006) OPTIMALITY OF RANDOMIZED TRUNK RESERVATION

"... We study an optimal admission of arriving customers to a Markovian finitecapacity queue, e.g. M/M/c/N queue, with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The goal is to maximize t ..."

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We study an optimal admission of arriving customers to a Markovian finitecapacity queue, e.g. M/M/c/N queue, with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The goal is to maximize the average rewards per unit time subject to the constraint on the average penalties per unit time. We provide a solution to this problem based on Lagrangian optimization. For a feasible problem, we show the existence of a randomized trunk reservation optimal policy with the acceptance thresholds for different customer types ordered according to a linear combination of the service rewards and rejection costs. In addition, we prove that any 1-randomized stationary optimal policy has this structure. In particular, we establish the structure of an optimal policy that maximizes the average rewards per unit time subject to the constraint on the blocking probability for one of the customer types or for a group of customer types pooled together.

### Optimal Wavelength Sharing Policies in OBS Networks Subject to QoS Constraints

"... Abstract — We consider the general problem of optimizing the performance of OBS networks with multiple traffic classes subject to strict (absolute) QoS constraints in terms of the end-toend burst loss rate of each guaranteed class of traffic. We employ Markov decision process (MDP) theory to obtain ..."

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Abstract — We consider the general problem of optimizing the performance of OBS networks with multiple traffic classes subject to strict (absolute) QoS constraints in terms of the end-toend burst loss rate of each guaranteed class of traffic. We employ Markov decision process (MDP) theory to obtain optimal wavelength sharing policies for two performance objectives, namely, maximization of weighted network throughput and minimization of the loss rate of best-effort traffic, while meeting the QoS guarantees. The randomized threshold policies we obtain are simple to implement and operate, and make effective use of statistical multiplexing. In particular, the threshold randomization feature enables the policies to allocate bandwidth at arbitrarily fine sub-wavelength granularity, hence making effective use of the available network capacity. Index Terms — Optical burst switching (OBS) networks, wavelength reservations, quality of service, Markov decision process, randomized threshold policies. I.

### Abstract

, 2005

"... We study optimal admission of arriving customers to a Markovian finite-capacity queue, e.g. M/M/c/N queue, with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The penalties are modelled ..."

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We study optimal admission of arriving customers to a Markovian finite-capacity queue, e.g. M/M/c/N queue, with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The penalties are modelled by a K-dimensional cost vector, K ≥ 1. The goal is to maximize the average rewards per unit time subject to the K constraints on the average costs per unit time. Let Km denote min{K, m − 1}, where m is the number of customer types. For a feasible problem, we show the existence of a Km-randomized trunk reservation optimal policy, where the acceptance thresholds for different customer types are ordered according to a linear combination of the service rewards and rejection costs. In addition, we prove that any Km-randomized stationary optimal policy has this structure. 1

### Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer

, 2005

"... Abstract. This paper studies a fluid queueing system that has a single server, a single finite buffer, and which applies a strict priority discipline to multiple arriving streams of different classes. The arriving streams are modeled by statistically independent, identically distributed random proce ..."

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Abstract. This paper studies a fluid queueing system that has a single server, a single finite buffer, and which applies a strict priority discipline to multiple arriving streams of different classes. The arriving streams are modeled by statistically independent, identically distributed random processes. A proof is presented for the highly intuitive result that, in such a queueing system, a higher priority class stream has a lower average fluid loss rate than a lower priority class stream. The proof exploits the fact that for a work-conserving queue, the fluid loss rate for a given class is invariant of what queueing discipline is applied to all arriving fluid of this particular class.