Higher Service Rate Research Articles

Priority assignment in queuing systems with unknown characteristics using learning automata and adaptive stochastic petri nets

In a queuing system with multiple queues and one server, a Priority Assignment (PA) mechanism is needed to assign the highest selection priority to the jobs from a class of jobs with the highest service rate. In this order, the shortest total waiting time of the system is achieved. The PA mechanism can be considered as an adaptive mechanism when some parameters of the queuing system, such as service rates, are unknown for this mechanism. In such queuing system, in order to the selection priorities to classes of jobs, an adaptive Probabilistic PA (PPA) mechanism can be utilized. The total waiting time of the queuing systems with unknown characteristics can be shortened by assigning the highest selection probability, rather than priority, to the jobs from a class of jobs with the highest service rate. In this paper, first Learning Automaton (LA) is introduced as an adaptive PPA mechanism in a queuing system with unknown characteristics consists of a server and m queues. Then, the proposed PPA mechanism is analyzed using a recently introduced model, which is the Adaptive Stochastic Petri Net (ASPN-LA). The results of this analysis enable us to establish a set of conditions for the termination of the adaptation in the LA-based mechanism. Thus, using this set of conditions, another adaptive mechanism is proposed, which consists of two phases: In the first phase, the LA is used to assign the selection probabilities to the classes of jobs and in the second phase, fixed levels of priorities are calculated using LA and then, instead of selection probabilistic, these priorities are used to select jobs for the service. The second phase of the mechanism is started when the proposed termination conditions are hold in the queuing system. Extensive computer simulations– reported in the paper –support the theoretical results. The results of these simulations indicate that the newly adaptive PPA mechanism with two phases is significantly better than or equal to the LA based PPA mechanism, over the average waiting time of the queuing system with three number of queues, in 86% of cases.

Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions

We study the equilibrium joining strategies for customers in an M/M/1 queue with working vacations and vacation interruptions. The service rate switches between a low and a high value depending on system dynamics. The server will take a multiple working vacation when the system is empty, during which a low service rate is provided to the arriving customers if any. Upon completion of the first customer’s service, given that the system is not empty, the working vacation will be terminated which means the server comes back and serves the following customers with a higher service rate. Otherwise, if the system is found empty upon completion of the first service, the server will continue his working vacation. Arriving customers may or may not know the state of the server and/or the number of the customers upon arrival, but they have to decide whether to enter the system or balk based on a linear reward-cost structure. We investigate customer behavior according to different levels of information regarding the system state. The equilibrium strategies for the customers are derived and the stationary behavior of the system under these strategies are analyzed. Finally, the effect of different levels of information on equilibrium thresholds and equilibrium entrance probabilities is illustrated by several numerical examples.

Stationary Analysis of Geo/Geo/1 Queue with Two-Speed Service and the Optimal Switching Threshold for the Service Rate

This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain threshold L, low service rate is provided for cost saving. On the other hand, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L. The steady-state probability distribution and the expected number of customers in the system are derived. Through the first-step argument, a recursive algorithm for computing the first moment of the conditional sojourn time is obtained. Furthermore, employing the results of regeneration cycle analysis, the direct search method is also implemented to determine the optimal value of L for minimizing the long-run average cost rate function.

Equilibrium Queueing Strategy of Loss-Averse Customers and Firms' Pricing Decisions

We consider a queueing system in which customers are loss averse towards both price and delay attributes: customers compare these two attributes to their rational expectations of the outcomes, with losses being more painful than equal-sized gains being pleasant. We first study customers' equilibrium queueing strategies. We find that, in contrast to the traditional case in which loss aversion is not considered, there could exist three equilibrium strategies, among which one is an evolutionarily stable strategy. We then study the optimal pricing problem for a monopoly server. We show that loss aversion polarizes queues, making long queues even longer and short queues even shorter. Furthermore, loss aversion towards the delay attribute drives down the optimal price whereas loss aversion towards the price attribute pushes up the optimal price. We also find that profit- and welfare-maximizing prices are not the same in a monopoly market. Finally we consider pricing competition in a duopoly market. We find that (1) in a symmetric duopoly setting, loss aversion can push up the equilibrium price; (2) in an asymmetric duopoly setting, the market share of the server with a higher service rate is larger than that in the traditional setting when loss aversion is not considered.

Maintenance of infinite-server service systems subjected to random shocks

Motivated by the need to study traffic incident management, we consider a Markovian infinite server queue that is subjected to randomly occurring shocks. These shocks affect the service of all servers to deteriorate, i.e., increase the service time of all servers, and might also cause other shocks, thus causing further service deterioration. There are a finite number of service levels, zero corresponding to the normal service with the highest service rate and the last level corresponding to the slowest service rate which could even be equal to zero, implying the complete service breakdown. The repair process is performed only at the last level. These types of queues also represent an approximation of multi-server call-centers with deteriorating service. We derive the mean and variance of the stationary number in the system, and show that the mean is convex with respect to the repair rate. Furthermore, we study the optimal repair rate that minimizes the expected long-run average cost incurred due to delay and repairs. We show that the expected total cost per unit time as a function of repair rate is unimodal. We derive conditions under which the cost function is in one of three simple forms, so that the optimum repair rate can easily be obtained. Numerical examples are also provided.

La diversificación y consolidación de los servicios sociales para las personas mayores en España y Suecia

La información sobre los servicios públicos para las personas mayores a menudo se limita a la atención residencial y a la ayuda a domicilio. Sin embargo, estos servicios básicos son en muchos países complementados o sustituidos por otros servicios de menor envergadura, como el transporte, comidas a domicilio, teleasistencia y centros de día. Esta diversificación partió de un racionamiento de los servicios para lograr una asignación más racional de los recursos y, si se podía, un menor gasto. En este trabajo se utilizan diversos datos sobre estos servicios en España y Suecia. Cuando se consideran todos los cuidados, la cobertura de atención es mucho mayor que si sólo se contemplan los servicios básicos. Esto indica una mayor consolidación de los mismos. Los datos sugieren mayor focalización en Suecia, y prestaciones fragmentadas en España, donde parece que los usuarios alcanzan lo disponible, con poca diferenciación entre sus necesidades. Cuando las tasas de cobertura son superiores, como en Suecia, hay mayor solapamiento entre el cuidado familiar y los servicios públicos. Con tasas más bajas, como en España, los cuidados familiares y los servicios públicos son sustitutos unos de otros. Se sugiere que una mayor diversidad de servicios, básicos y secundarios, puede adaptarse mejor y de manera más eficiente a las diversas necesidades de las personas mayores que la elección entre ningún servicio, ayuda domiciliaria o atención residencial. Aunque estos servicios secundarios también puedan ser utilizados como un sustituto de bajo coste, e inferior calidad, en la atención.

Diversification and strengthening of services for older people in Spain and Sweden

Information on public services for older people is often limited to institutional care and Home Help/Home Care, be it for individuals in surveys, statistics for a specific country or for international comparisons. Yet, these two major services are in many countries supplemented - or substituted - by other, minor services. The latter include services such as transportation services, meals-on-wheels, alarm systems and day care. This diversification is the outcome of a rationing of services to achieve a more rational allocation of resources and attempts to keep down costs. In this presentation we use various data sources to provide information on all these types of support for Spain and Sweden. When all of them are considered, service coverage is much higher than by basic services alone, indicating further consolidation of services. Data suggests a high targeting in Sweden, but fragmented delivery in Spain, where - we suspect-users get what is available, with little differentiation between needs. With higher service rates, as in Sweden, there is greater overlap between family care and public services; with lower coverage rates, as in Spain, family care and public services are more often substituted for each other. It is suggested that a range of services, major and minor, may suit the varying needs of older people better - and more efficiently-than the choice between nothing, Home Help or institutional care, but that minor services may also be used as an inexpensive - and sometimes inferior-substitute for full support.

Function Assessment of Online Game Websites in Great China Area

The purpose of this study is to develop a content architecture for analyzing the functions of online game websites and their revenue sources based on Angehrn's virtual spaces of ICDT model: virtual information space (VIS), virtual communication space (VCS), virtual distribution space (VDS) and virtual transaction space (VTS). A content architecture based on ICDT was constructed and employed to analyze 26 online game websites chosen from top online game rankings in Mainland China, Hong Kong, and Taiwan. This research found that websites in China area provide the highest service rate in VCS; those in Hong Kong area provide the highest service rate in VIS; Taiwan's online game websites provide the highest service rate in VTS and VDS. Most of the websites investigated provide good service functions in VIS, but require further improvement of their VTS functions in the Great China area. The findings in this study can help understand the current status of online game websites in Great China area and can also be used for website owners to improve web design by offering players more decent function services.

Large Deviations Sum-Queue Optimality of a Radial Sum-Rate Monotone Opportunistic Scheduler

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">maximizing current service rate</i> (being opportunistic) versus <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">balancing unequal queues</i> (enhancing user-diversity to enable future high service rate opportunities). By contrast, with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sum-rate monotonic (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper, it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a two-queue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.

Cross-layer Optimized Vertical Handover Schemes between Mobile WiMAX and 3G Networks

Nowadays, wireless packet data services are provided over Wireless MAN (WMAN) at a high data service rate, while 3G cellular networks provide wide-area coverage at a low data service rate. The integration of mobile WiMAX and 3G networks is essential, to serve users requiring both high-speed wireless access as well as wide-area connectivity. In this paper, we propose a cross-layer optimization scheme for a vertical handover between mobile WiMAX and 3G cellular networks. More specifically, L2 (layer 2) and L3 (layer 3) signaling messages for a vertical handover are analyzed and reordered/combined, to optimize the handover procedure. Extensive simulations using ns-2 demonstrate that the proposed scheme enhances the performance of a vertical handover between mobile WiMAX and 3G networks: low handover latency, high TCP throughput, and low UDP packet loss ratio.

Extremal properties of the FIFO discipline in queueing networks

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons:(i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means.(ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means.We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR.Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

Extremal properties of the FIFO discipline in queueing networks

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons: (i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means. (ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means. We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR. Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.