Performance Approximation and Design of Pick-and-Pass Order Picking Systems

In this paper, we discuss an approximation method based on G/G/m queuing network modeling using Whitt’s (1983) queuing network analyzer to analyze pick-and-pass order picking systems. The objective of this approximation method is to provide an instrument for obtaining rapid performance estimates (such as order lead time and station utilization) of the order picking system. The pick-and-pass system is decomposed into conveyor pieces and pick stations. Conveyor pieces have a constant processing time, whereas the service times at a pick station depend on the number of order lines in the order to be picked at the station, the storage policy at the station, and the working methods. Our approximation method appears to be sufficiently accurate for practical purposes. It can be used to rapidly evaluate the effects of the storage methods in pick stations, the number of order pickers at stations, the size of pick stations, the arrival process of customer orders, and the impact of batching and splitting orders on system performance.simulation;warehousing;order picking;queuing network;pick-and-pass

Towards a unifying theory on branching-type polling systems in heavy traffic

For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Performance Approximation and Design of Pick-and-Pass Order Picking Systems

In this paper, we discuss an approximation method based on G/G/m queuing network modeling using Whitt’s (1983) queuing network analyzer to analyze pick-and-pass order picking systems. The objective of this approximation method is to provide an instrument for obt

Towards a unifying theory on branching-type polling models in heavy traffic

htmlabstractFor a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Next generation communications satellites: multiple access and network studies

Efficient resource allocation and network design for satellite systems serving heterogeneous user populations with large numbers of small direct-to-user Earth stations are discussed. Focus is on TDMA systems involving a high degree of frequency reuse by means of satellite-switched multiple beams (SSMB) with varying degrees of onboard processing. Algorithms for the efficient utilization of the satellite resources were developed. The effect of skewed traffic, overlapping beams and batched arrivals in packet-switched SSMB systems, integration of stream and bursty traffic, and optimal circuit scheduling in SSMB systems: performance bounds and computational complexity are discussed

Performance Evaluation of Transition-based Systems with Applications to Communication Networks

Since the beginning of the twenty-first century, communication systems have witnessed a revolution in terms of their hardware capabilities. This transformation has enabled modern networks to stand up to the diversity and the scale of the requirements of the applications that they support. Compared to their predecessors that primarily consisted of a handful of homogeneous devices communicating via a single communication technology, today's networks connect myriads of systems that are intrinsically different in their functioning and purpose. In addition, many of these devices communicate via different technologies or a combination of them at a time. All these developments, coupled with the geographical disparity of the physical infrastructure, give rise to network environments that are inherently dynamic and unpredictable. To cope with heterogeneous environments and the growing demands, network units have taken a leap from the paradigm of static functioning to that of adaptivity. In this thesis, we refer to adaptive network units as transition-based systems (TBSs) and the act of adapting is termed as transition. We note that TBSs not only reside in diverse environment conditions, their need to adapt also arises following different phenomena. Such phenomena are referred to as triggers and they can occur at different time scales. We additionally observe that the nature of a transition is dictated by the specified performance objective of the relevant TBS and we seek to build an analytical framework that helps us derive a policy for performance optimization. As the state of the art lacks a unified approach to modelling the diverse functioning of the TBSs and their varied performance objectives, we first propose a general framework based on the theory of Markov Decision Processes. This framework facilitates optimal policy derivation in TBSs in a principled manner. In addition, we note the importance of bespoke analyses in specific classes of TBSs where the general formulation leads to a high-dimensional optimization problem. Specifically, we consider performance optimization in open systems employing parallelism and closed systems exploiting the benefits of service batching. In these examples, we resort to approximation techniques such as a mean-field limit for the state evolution whenever the underlying TBS deals with a large number of entities. Our formulation enables calculation of optimal policies and provides tangible alternatives to existing frameworks for Quality of Service evaluation. Compared to the state of the art, the derived policies facilitate transitions in Communication Systems that yield superior performance as shown through extensive evaluations in this thesis

Scheduling policies for disks and disk arrays

Recent rapid advances of magnetic recording technology have enabled substantial increases in disk capacity. There has been less than 10% improvement annually in the random access time to small data blocks on the disk. Such accesses are very common in OLTP applications, which tend to have stringent response time requirements. Scheduling of disk requests is intended to improve their response time, reduce disk service time, and increase disk access bandwidth with respect to the default FCFS scheduling policy. Shortest Access Time First policy has been shown to outperform other classical disk scheduling policies in numerous studies. Before verifying this conclusion, this dissertation develops an empirical analysis of the SATF policy, and produces a valuable by-product, expressed as x[m] = mp, during the study. Classical scheduling policies and some well-known variations of the SATE policy are re-evaluated, and three extensions are proposed. The performance evaluation uses self-developed simulators containing detailed disk information. The simulators, driven with both synthetic and trace workloads, report the measurements of requests, such as the mean and the 95th percentile of the response times, as well as the measurements of the system, such as the maximum throughput. A comprehensive arrangement of routing and scheduling schemes is presented or mirrored disk systems, or RAIDi. The performance evaluation is based on a twodimensional configuration classification: independent queues (i.e. a router sends the requests to one of the disks as soon as these requests arrive) versus a shared queue (i.e. the requests are held in a common queue at the router and are scheduled to be served); normal data layout versus transposed data layout (i.e. the data stored on the inner cylinders of one disk is duplicated on the outer cylinders of the mirrored disk). The availability of a non-volatile storage or NVS, which allows the processing of write requests to be deferred, is also investigated. Finally, various strategies of mirrored disk declustering are compared against the basic disk mirroring. Their competence of load balancing and their reliability are examined in both normal mode and degraded mode

Integrated Analytical Performance Evaluation Models of Warehouses

Warehouse design process is a complex process with numerous alternatives at all design stages, with focus on throughput capacity, inventory size and material handling equipment requirements. Enumerating all feasible solutions that satisfy the throughput and storage capacity requirements is not practical. Analytical models play a key role in the preliminary design stages in identifying several good initial warehouse configurations. This research effort pertains to the development of integrated analytical models that address capacity/congestion and inventory issues simultaneously in warehouse systems.The first part of the dissertation focuses on the development of a queueing network model of the "shared-server system," which is an inventory store with a server performing both storage and retrieval operations. First, we modeled the shared-server system using Continuous Time Markov Chains (CTMC) under exponential assumptions. We then developed an approximate queueing network model for general arrivals and general service time distribution, and designed a solution procedure based on the parametric-decomposition method. Later, we extended these models to include multi-server cases.The second part of the dissertation focuses on the development of a queueing-inventory (QI) model of an order-picking system. The configuration of the unit-load that is stored (pallets) is different from that which is retrieved (cases). We developed a single stage QI model with batch processing to represent the material movement in and out of the forward inventory store. We then extended these models to include multi-server cases.The last part of the dissertation focuses on the development of an integrated model that demonstrates the applicability of these key building blocks (the shared-server system and the order-picking system) in developing an end-to-end model of the warehouse system. Extensive numerical experiments indicate that the proposed analytical models can be solved in a computationally efficient manner and are accurate for a wide range of parameter values when compared with simulation estimates.Industrial Engineering & Managemen

Tradeoffs between Anonymity and Quality of Services in Data Networking and Signaling Games

Timing analysis has long been used to compromise users\u27 anonymity in networks. Even when data is encrypted, an adversary can track flows from sources to the corresponding destinations by merely using the correlation between the inter-packet timing on incoming and outgoing streams at intermediate routers. Anonymous network systems, where users communicate without revealing their identities, rely on the idea of Chaum mixing to hide `networking information\u27. Chaum mixes are routers or proxy servers that randomly reorder the outgoing packets to prevent an eavesdropper from tracking the flow of packets. The effectiveness of such mixing strategies is, however, diminished under constraints on network Quality of Services (QoS)s such as memory, bandwidth, and fairness. In this work, two models for studying anonymity, packet based anonymity and flow based anonymity, are proposed to address these issues quantitatively and a trade-off between network constraints and achieved anonymity is studied. Packet based anonymity model is proposed to study the short burst traffic arrival models of users such as in web browsing. For packet based anonymity, an information theoretic investigation of mixes under memory constraint and fairness constraint is established. Specifically, for memory constrained mixes, the first single letter characterization of the maximum achievable anonymity for a mix serving two users with equal arrival rates is provided. Further, for two users with unequal arrival rates the anonymity is expressed as a solution to a series of finite recursive equations. In addition, for more than two users and arbitrary arrival rates, a lower bound on the convergence rate of anonymity is derived as buffer size increases and it is shown that under certain arrival configurations the lower bound is tight. The adverse effects of requirement of fairness in data networking on anonymous networking is also studied using the packet based anonymity model and a novel temporal fairness index is proposed to compare the tradeoff between fairness and achieved anonymity of three diverse and popular fairness paradigms: First Come First Serve, Fair Queuing and Proportional Method. It is shown that FCFS and Fair Queuing algorithms have little inherent anonymity. A significant improvement in anonymity is therefore achieved by relaxing the fairness paradigms. The analysis of the relaxed FCFS criterion, in particular, is accomplished by modeling the problem as a Markov Decision Process (MDP). The proportional method of scheduling, while avoided in networks today, is shown to significantly outperform the other fair scheduling algorithms in anonymity, and is proven to be asymptotically optimal as the buffer size of the scheduler is increased. Flow based anonymity model is proposed to study long streams traffic models of users such as in media streaming. A detection theoretic measure of anonymity is proposed to study the optimization of mixing strategies under network constraints for this flow based anonymity model. Specifically, using the detection time of the adversary as a metric, the effectiveness of mixing strategies is maximized under constraints on memory and throughput. A general game theoretic model is proposed to study the mixing strategies when an adversary is capable of capturing a fraction of incoming packets. For the proposed multistage game, existence of a Nash equilibrium is proven, and the optimal strategies for the mix and adversary were derived at the equilibrium condition.It is noted in this work that major literature on anonymity in Internet is focused on achieving anonymity using third parties like mixes or onion routers, while the contributions of users\u27 individual actions such as accessing multiple websites to hide the targeted websites, using multiple proxy servers to hide the traffic routes are overlooked. In this thesis, signaling game model is proposed to study specifically these kind of problems. Fundamentally, signaling games consist of two players: senders and receivers and each sender belongs to one of multiple types. The users who seek to achieve anonymity are modeled as the sender of a signaling game and their types are identified by their personal information that they want to hide. The eavesdroppers are modeled as the receiver of the signaling game. Senders transmit their messages to receivers. The transmission of these messages can be seen as inevitable actions that a user have to take in his/her daily life, like the newspapers he/she subscribes on the Internet, online shopping that he/she does, but these messages are susceptible to reveal the user identity such as his/her political affiliation or his/her affluence level. The receiver (eavesdropper) uses these messages to interpret the senders\u27 type and take optimal actions according to his belief of senders\u27 type. Senders choose their messages to increase their reward given that they know the optimal policies of the receivers for choosing the action based on the transmitted message. However, sending the messages that increases senders\u27 reward may reveal their type to receivers thus violating their privacy and can be used by eavesdropper in future to harm the senders. In this work, the payoff of a signalling game is adjusted to incorporate the information revealed to an eavesdropper such that this information leakage is minimized from the users\u27 perspective. The existence of Bayesian-Nash equilibrium is proven in this work for the signaling games even after the incorporation of users\u27 anonymity. It is also proven that the equilibrium point is unique if the desired anonymity is below a certain threshold

Entropy Maximisation and Queues With or Without Balking. An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks.

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusion