Queueing System with Potential for Recruiting Secondary Servers

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD-type queue. However, one can also study this model as a G I/M/1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented

(R1975) MAP/PH(1), PH(2)/2 Queue with Multiple Vacation, Optional Service, Consultations and Interruptions

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s waiting time distribution has been examined in more detail during the busy times. The system’s key parameters are assessed, and a few graphs and numerical representations are constructed

(R2051) Analysis of MAP/PH1, PH2/2 Queueing Model with Working Breakdown, Repairs, Optional Service, and Balking

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service when the moment of server-2 struck with breakdown. In the period of vacation/closedown of server-1 and the server-2 is in working breakdown or under repair process, the arrival of customers may balk the system due to the impatient. Stability conditions has derived for our system and the stationary probability vector was evaluated by using the matrix analytical method. This model also examined at the analysis of busy period,waiting time distribution and system performance measures. The numerical illustrations are provided with the aid of two dimensional and three dimensional graphs

Order acceptance with reinforcement learning

Order Acceptance (OA) is one of the main functions in a business control framework. Basically, OA involves for each order a 0/1 (i.e., reject/accept) decision. Always accepting an order when capacity is available could unable the system to accept more convenient orders in the future. Another important aspect is the aV'(tiiability of information to the decisionmaker. We use a stochastic modeling approach using Markov decision theory and learning methods from Artificial Intelligence techniques in order to deal with uncertainty and long-term decisions in Ok Reinforcement Learning (RL) is a quite new approach that already combines this idea of modeling and solution method. Here we report on RL-solutions for some OA models

Revenue maximization problems in commercial data centers

PhD ThesisAs IT systems are becoming more important everyday, one of the main concerns is that users may face major problems and eventually incur major costs if computing systems do not meet the expected performance requirements: customers expect reliability and performance guarantees, while underperforming systems loose revenues. Even with the adoption of data centers as the hub of IT organizations and provider of business efficiencies the problems are not over because it is extremely difficult for service providers to meet the promised performance guarantees in the face of unpredictable demand. One possible approach is the adoption of Service Level Agreements (SLAs), contracts that specify a level of performance that must be met and compensations in case of failure. In this thesis I will address some of the performance problems arising when IT companies sell the service of running ‘jobs’ subject to Quality of Service (QoS) constraints. In particular, the aim is to improve the efficiency of service provisioning systems by allowing them to adapt to changing demand conditions. First, I will define the problem in terms of an utility function to maximize. Two different models are analyzed, one for single jobs and the other useful to deal with session-based traffic. Then, I will introduce an autonomic model for service provision. The architecture consists of a set of hosted applications that share a certain number of servers. The system collects demand and performance statistics and estimates traffic parameters. These estimates are used by management policies which implement dynamic resource allocation and admission algorithms. Results from a number of experiments show that the performance of these heuristics is close to optimal.QoSP (Quality of Service Provisioning)British Teleco

Performability modelling of homogenous and heterogeneous multiserver systems with breakdowns and repairs

This thesis presents analytical modelling of homogeneous multi-server systems with reconfiguration and rebooting delays, heterogeneous multi-server systems with one main and several identical servers, and farm paradigm multi-server systems. This thesis also includes a number of other research works such as, fast performability evaluation models of open networks of nodes with repairs and finite queuing capacities, multi-server systems with deferred repairs, and two stage tandem networks with failures, repairs and multiple servers at the second stage. Applications of these for the popular Beowulf cluster systems and memory servers are also accomplished. Existing techniques used in performance evaluation of multi-server systems are investigated and analysed in detail. Pure performance modelling techniques, pure availability models, and performability models are also considered. First, the existing approaches for pure performance modelling are critically analysed with the discussions on merits and demerits. Then relevant terminology is defined and explained. Since the pure performance models tend to be too optimistic and pure availability models are too conservative, performability models are used for the evaluation of multi-server systems. Fault-tolerant multi-server systems can continue service in case of certain failures. If failure does not occur at a critical point (such as breakdown of the head processor of a farm paradigm system) the system continues serving in a degraded mode of operation. In such systems, reconfiguration and/or rebooting delays are expected while a processor is being mapped out from the system. These delay stages are also taken into account in addition to failures and repairs, in the exact performability models that are developed. Two dimensional Markov state space representations of the systems are used for performability modelling. Following the critical analysis of the existing solution techniques, the Spectral Expansion method is chosen for the solution of the models developed. In this work, open queuing networks are also considered. To evaluate their performability, existing modelling approaches are expanded and validated by simulations, for performability analysis of multistage open networks with finite queuing capacities. The performances of two extended modelling approaches are compared in terms of accuracy for open networks with various queuing capacities. Deferred repair strategies are becoming popular because of the cost reductions they can provide. Effects of using deferred repairs are analysed and performability models are provided for homogeneous multi-server systems and highly available farm paradigm multi-server systems. Since one of the random variables is used to represent the number of jobs in one of the queues, analytical models for performance evaluation of two stage tandem networks suffer because of numerical cumbersomeness. Existing approaches for modelling these systems are actually pure performance models since breakdowns and repairs cannot be considered. One way of modelling these systems can be to divide one of the random variables to present both the operative and non-operative states of the server in one dimension. However, this will give rise to state explosion problem severely limiting the maximum queue capacity that can be handled. In order to overcome this problem a new approach is presented for modelling two stage tandem networks in three dimensions. An approximate solution is presented to solve such a system. This approach manifests itself as a novel contribution for alleviating the state space explosion problem for large and/or complex systems. When two state tandem networks with feedback are modelled using this approach, the operative states can be handled independently and this makes it possible to consider multiple operative states at the second stage. The analytical models presented can be used with various parameters and they are extendible to consider systems with similar architectures. The developed three dimensional approach is capable to handle two stage tandem networks with various characteristics for performability measures. All the approaches presented give accurate results. Numerical solutions are presented for all models developed. In case the solution presented is not exact, simulations are performed to validate the accuracy of the results obtained

Approximate Analysis of an Unreliable M/M/2 Retrial Queue

This thesis considers the performance evaluation of an M/M/2 retrial queue for which both servers are subject to active and idle breakdowns. Customers may abandon service requests if they are blocked from service upon arrival, or if their service is interrupted by a server failure. Customers choosing to remain in the system enter a retrial orbit for a random amount of time before attempting to re-access an available server. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure. Interfailure times, repair times and times between retrials are exponentially distributed, and all processes are assumed to be mutually independent. Modeling the number of customers in the orbit and status of the servers as a continuous-time Markov chain, we employ a phase-merging algorithm to approximately analyze the limiting behavior. Subsequently, we derive approximate expressions for several congestion and delay measures. Using a benchmark simulation model, we assess the accuracy of the approximations and show that, when the algorithm assumptions are met, the approximation procedure yields favorable results. However, as the rate of abandonment for blocked arrivals decreases, the performance declines while the results are insensitive to the rate of abandonment of customers preempted by a server failure

Queueing Models and Assessment Tools for Improving Mass Dispensing and Vaccination Clinic Planning

To react to an outbreak of a contagious disease that requires medication or vaccination, county health departments must set up and operate mass dispensing and vaccination centers, commonly known as points of dispensing (PODs), to treat residents who may be affected. Carefully planning these PODs before an event occurs is a difficult and important job. Simulation models can provide an accurate representation of resident flow through PODs, but are not convenient for public health professionals to access. Queueing theory provides a multitude of analytical models appropriate for various situations so many models that it is often difficult to discern which model is correct for a particular circumstance. There are also some situations for which no models are available, particularly those involving batching and multiple servers. A complete set has been gathered of those models that are the most generalized, and hence useful for the widest range of applications. Where no appropriate model was available, modifications to the existing equations are proposed and tested. To implement this general queueing framework, software has been developed which can quickly generate planning models using steady-state queueing network approximations; these models use commonly available spreadsheet software to maximize accessibility for public health emergency planners. The planning models are validated against models created in several queueing software packages, along with simulation models automatically generated from the planning models. The number of stations and staff within a POD are not the only concerns that a public health emergency preparedness and response plan must address. A plan assessment tool is proposed, which can help planners ensure that their POD plans include all relevant information. A layout assessment tool is also developed, which endeavors to give planners suggestions on how to design PODs for maximum efficiency

Self-Service System with Rating Dependent Arrivals

A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided