On completion times in a two-class priority queue with impatience loane Muni Toke

Abstract: In this note, we consider a two-class priority queueing system with Poisson arrivals, general service time distribution and one server, in which customers that are not currently being served may leave the queue according to exponentially distributed patience times, i.e., a M 1 , M 2 /G/1 + M system using a generalised Kendall's notation. We expand the classic methodology to derive analytical formulas for the completion times in such a system, using preemptive repeat different and preemptive repeat identical disciplines. Known average completion times for priority queues without impatience are retrieved as limit cases. Keywords: priority queues; queues with impatience; reneging; completion times; preemptive disciplines. Reference to this paper should be made as follows: Toke, I.M. (2014) 'On completion times in a two-class priority queue with impatience', Int

A Non-Markovian Multistage Batch Arrival Queue with Breakdown and Reneging

The present investigation deals with analysis of non-Markovian queueing model with multistage of services. When the server is unavailable during the system breakdown (or) vacation periods, we consider reneging to prevail. Supplementary variable techniques have been adopted to obtain steady state system length distributions. The numerical illustrations are provided to validate the tractability of performance measures as far as computational aspect is concerned. Numerical results in the form of graphical representation are also presented. Practical large scale industry applications are described to justify our model

Routing and transfers amongst parallel queues

This thesis is concerned with maximizing the performance of policies for routing and transferring jobs in systems of heterogeneous servers. The tools used are probabilistic modelling, optimization and simulation. First, a system is studied where incoming jobs are allocated to the queue belonging to one of a number of servers, each of which goes through alternating periods of being operative and inoperative. The objective is to evaluate and optimize performance and cost metrics. Jobs incur costs for the amount of time that they spend in a queue, before commencing service. The optimal routing policy for incoming jobs is obtained by solving numerical programming equations. A number of heuristic policies are compared against the optimal, and one dynamic routing policy is shown to perform well over a large range of parameters. Next, the problem of how best to deal with the transfer of jobs is considered. Jobs arrive externally into the queue attached to one of a number of servers, and on arrival are assigned a time-out period. Jobs whose time-out period expires before it commences service is instantaneously transferred to the end another queue, based on a routing policy. Upon transfer, a transfer cost is incurred. An approximation to the optimal routing policy is computed, and compared with a number of heuristic policies. One heuristic policy is found to perform well over a large range of parameters. The last model considered is the case where incoming jobs are allocated to the queue attached to one of a number of servers, each of which goes through periods of being operative and inoperative. Additionally, each job is assigned a time-out on arrival into a queue. Any job whose time-out period expires before it commences service is instantaneously transferred to the end of another queue, based on a transfer policy. The objective is to evaluate and optimize performance and cost metrics. Jobs incur costs for the amount of time that they spend in a queue, before commencing service, and additionally incur a cost for each transfer they experience. A number of heuristic transfer policies are evaluated and one heuristic which performs for a wide range of parameters is observed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Impact of Mobility and Wireless Channel on the Performance of Wireless Networks

This thesis studies the impact of mobility and wireless channel characteristics, i. e. , variability and high bit-error-rate, on the performance of integrated voice and data wireless systems from network, transport protocol and application perspectives. From the network perspective, we study the impact of user mobility on radio resource allocation. The goal is to design resource allocation mechanisms that provide seamless mobility for voice calls while being fair to data calls. In particular, we develop a distributed admission control for a general integrated voice and data wireless system. We model the number of active calls in a cell of the network as a Gaussian process with time-dependent mean and variance. The Gaussian model is updated periodically using the information obtained from neighboring cells about their load conditions. We show that the proposed scheme guarantees a prespecified dropping probability for voice calls while being fair to data calls. Furthermore, the scheme is stable, insensitive to user mobility process and robust to load variations. From the transport protocol perspective, we study the impact of wireless channel variations and rate scheduling on the performance of elastic data traffic carried by TCP. We explore cross-layer optimization of the rate adaptation feature of cellular networks to optimize TCP throughput. We propose a TCP-aware scheduler that switches between two rates as a function of TCP sending rate. We develop a fluid model of the steady-state TCP behavior for such a system and derive analytical expressions for TCP throughput that explicitly account for rate variability as well as the dependency between the scheduler and TCP. The model is used to choose RF layer parameters that, in conjunction with the TCP-aware scheduler, improve long-term TCP throughput in wireless networks. A distinctive feature of our model is its ability to capture variability of round-trip-time, channel rate and packet error probability inherent to wireless communications. From the application perspective, we study the performance of wireless messaging systems. Two popular wireless applications, the short messaging service and multimedia messaging service are considered. We develop a mathematical model to evaluate the performance of these systems taking into consideration the fact that each message tolerates only a limited amount of waiting time in the system. Using the model, closed-form expressions for critical performance parameters such as message loss, message delay and expiry probability are derived. Furthermore, a simple algorithm is presented to find the optimal temporary storage size that minimizes message delay for a given set of system parameters

Aggregation Approaches for Incorporating E-mail Processing History in Queueing Models of Customer Contact Centers

The operation of a customer contact center where the interface between the agents' and the customer happens through e-mail was modeled using a multi-class open queueing network model. A novel approach to model the dependence of processing times and routing on e-mail history called the history-based aggregation method was developed. This aggregation method extends the popular parametric decomposition (PD) method for solving multi-class open queueing networks to more general situations. A discrete-time Markov chain (DTMC) with an expanded state space was developed to model the non-Markovian routing of a new e-mail through the contact center until its eventual resolution. The analysis of this absorbing Markov chain led to the computation of the proportion of e-mails in an agent's in-box that are new, previously processed by the same agent, or previously processed by another agent. Using these proportions, a new "history-based" aggregation step for each customer class in the PD method was introduced. This step precedes the existing class-based aggregation step in the PD method. The resulting queueing network model was solved using the RAQS software package. The accuracy and robustness of the analytical approach was demonstrated by comparing the analytical results with simulation estimates of performance measures for a variety of scenarios. Typical contact center situations like grouping of agents and server interruptions were also modeled within the above approach. The DTMC-based analytical method showed excellent prediction capability across the various cased examined. The relative percentage error in utilization was less than 1% in all cases and less than 17% for other performance measures. This work has laid the foundation for the development of rapid performance analysis tools for customer contact centers which can be effectively used for improving customer contact center operations. The history-based aggregation method represents a significant extension to the PD method for solving queueing network models.Industrial Engineering & Managemen

Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs