Queueing Models with MAP Arrivals Useful in Service Sectors

Queueing models have found applications in many fields, notably in service sectors. In this paper, we study queueing models that have significant applications in service sectors. We look at multi-server systems with MAP arrivals. We assume phase type services for single server systems and exponential services when dealing with multi-server systems. All arriving customers finding no idle server will not wait in the system to receive services but rather leave their information in a registry list. These customers will be reached out on a first-come-first-served basis (FCFS) by an idle server soon after completing its current service. The reach out time is assumed to be exponential and at the end of this time, with a certain probability the reached out customer is available for service; with complementary probability the customer is not reachable due to various reasons including the customer not picking up the call from the service system to receive a service. In the case when the reach out is unsuccessful, the server will remain idle should there be no customer in the registry list. However, if there is at least one customer in the registry, then the server will start another reach out. The classical approach using matrix-analytic methods is employed and discuss a few illustrative examples that bring out the qualitative nature of the models in steady-state. When dealing with MAP/G/c queues we resort to simulation and present a few examples. Some concluding remarks including a few extensions to the models studied here are presented

Call centers with a postponed callback offer

We study a call center model with a postponed callback option. A customer at the head of the queue whose elapsed waiting time achieves a given threshold receives a voice message mentioning the option to be called back later. This callback option differs from the traditional ones found in the literature where the callback offer is given at customer’s arrival. We approximate this system by a two-dimensional Markov chain, with one dimension being a unit of a discretization of the waiting time. We next show that this approximation model converges to the exact one. This allows us to obtain explicitly the performance measures without abandonment and to compute them numerically otherwise. From the performance analysis, we derive a series of practical insights and recommendations for a clever use of the callback offer. In particular, we show that this time-based offer outperforms traditional ones when considering the waiting time of inbound calls

On-board B-ISDN fast packet switching architectures. Phase 2: Development. Proof-of-concept architecture definition report

For the next-generation packet switched communications satellite system with onboard processing and spot-beam operation, a reliable onboard fast packet switch is essential to route packets from different uplink beams to different downlink beams. The rapid emergence of point-to-point services such as video distribution, and the large demand for video conference, distributed data processing, and network management makes the multicast function essential to a fast packet switch (FPS). The satellite's inherent broadcast features gives the satellite network an advantage over the terrestrial network in providing multicast services. This report evaluates alternate multicast FPS architectures for onboard baseband switching applications and selects a candidate for subsequent breadboard development. Architecture evaluation and selection will be based on the study performed in phase 1, 'Onboard B-ISDN Fast Packet Switching Architectures', and other switch architectures which have become commercially available as large scale integration (LSI) devices

Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic

A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the system's state. We examine two versions of the problem: ``nonpreemptive,'' where service is uninterruptible, and ``preemptive,'' where service to a customer can be interrupted and then resumed, possibly at a different station. We study the problem in the asymptotic heavy traffic regime proposed by Halfin and Whitt, in which the arrival rates and the number of servers at each station grow without bound. The two versions of the problem are not, in general, asymptotically equivalent in this regime, with the preemptive version showing an asymptotic behavior that is, in a sense, much simpler. Under appropriate assumptions on the structure of the system we show: (i) The value function for the preemptive problem converges to $V$, the value of a related diffusion control problem. (ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$. The construction of these policies is based on a Hamilton--Jacobi--Bellman equation associated with $V$.Comment: Published at http://dx.doi.org/10.1214/105051605000000601 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quality of Service over Specific Link Layers: state of the art report

The Integrated Services concept is proposed as an enhancement to the current Internet architecture, to provide a better Quality of Service (QoS) than that provided by the traditional Best-Effort service. The features of the Integrated Services are explained in this report. To support Integrated Services, certain requirements are posed on the underlying link layer. These requirements are studied by the Integrated Services over Specific Link Layers (ISSLL) IETF working group. The status of this ongoing research is reported in this document. To be more specific, the solutions to provide Integrated Services over ATM, IEEE 802 LAN technologies and low-bitrate links are evaluated in detail. The ISSLL working group has not yet studied the requirements, that are posed on the underlying link layer, when this link layer is wireless. Therefore, this state of the art report is extended with an identification of the requirements that are posed on the underlying wireless link, to provide differentiated Quality of Service

XSnap : a queueing network analysis package

Bibliography: pages 114-116.This dissertation describes the design and implementation of a sophisticated X-Windows based modelling package called XSnap, which can be used to solve product-form mixed multi-class queueing networks. A Graphical User Interface allows interactive network specification, whilst the modeller can also define complex network experiments and request customised output through the use of a language called SnapL. The solution modules used by XSnap are grouped together to form the Calculation Modules ToolBox (CMTB), which can be easily integrated into any modelling package which provides an appropriate user interface. Solution statistics are found using Reiser's Mean Value Analysis (MVA) algorithm, which has been extended to allow for the approximate solution of networks with PRIORITY servers or non-integral closed chain populations. A routing validation algorithm is used to validate the routing information for the network to be solved, and equations defining the relative throughput (or visit ratio) of each class at each centre in the network, are solved using a version of LU-Decomposition called Crout's method with partial pivoting. The dissertation also includes a study of a number of other available modelling packages. The choice of features included in the XSnap GUI has been largely influenced by this study. A number of different algorithms for solving product-form queueing networks are also discussed, and relevant points from this discussion are presented as part of the motivation for using the MVA algorithm for finding solution statistics

Programming Protocol-Independent Packet Processors

P4 is a high-level language for programming protocol-independent packet processors. P4 works in conjunction with SDN control protocols like OpenFlow. In its current form, OpenFlow explicitly specifies protocol headers on which it operates. This set has grown from 12 to 41 fields in a few years, increasing the complexity of the specification while still not providing the flexibility to add new headers. In this paper we propose P4 as a strawman proposal for how OpenFlow should evolve in the future. We have three goals: (1) Reconfigurability in the field: Programmers should be able to change the way switches process packets once they are deployed. (2) Protocol independence: Switches should not be tied to any specific network protocols. (3) Target independence: Programmers should be able to describe packet-processing functionality independently of the specifics of the underlying hardware. As an example, we describe how to use P4 to configure a switch to add a new hierarchical label

Implementing a service software to relieve waiting line frustration

Service companies have used waiting lines as a way of buffering the constant flow of providing a service for a long time. The introduction of hurdles, line numbers, time based appointments and virtualization have all worked for better and faster service, but the problem of long waiting lines has so far not been solved. The subject of this work is a startup company which has built a queue management service that enables smartphone users to wait in line remotely. The startup team to which I belong has built a product around the promise of allowing people to use the waiting time in their own terms. Therefore making the the issue of long period between request for service and actual service less important from customer perspective. By developing a minimum viable product for validating the market we have discovered that the customer pain of long queues does not convert into service provider’s pain: the combination of long waiting time, recurrence of the wait and option for replacement are rare combination that exists only on theoretical level. This work will concentrate on the findings on introducing new technology of remote queuing to the market and the specifics of waiting lines and the conditions where this technology would be most adaptable. This study maps out all the methods the team used for introducing the technology, all the findings and the conclusions that were made during the process. By testing different methods a model was developed that describes the problems of introducing new technologies that require personal hardware support from both parties in the context of physical serviceshttp://tartu.ester.ee/record=b2656163~S1*est2023-05-0