A Polling-Based Dynamic Order-Picking System considering Priority Orders

Nowadays, how to offer extremely fast response to customer orders has become a major challenge for warehouse management, especially in e-commerce. Due to the time urgency aspect of some “VIP” orders that need priority processing, one of the most important issues for logistics distribution centres is how to improve the VIP order-picking priority without reducing the common order-picking efficiency. With this consideration, this article put forward a new priority polling model to describe and analyse this problem. We divide orders into priority and common categories according to their time urgency. A mathematical model is established for such a system by applying polling theory, a probability generating function, and an embedded Markov chain. Numerical analysis shows that this priority polling-based picking system can improve the picking efficiency and is well suited to practical operations.

An asymptotic property of branching-type overloaded polling networks

Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] studied the fluid asymptotics of the joint queue length process for an overloaded cyclic polling system with multigated service discipline by exploiting the connection with multi-type branching processes. In contrast to the heavy traffic behaviors, the cycle time of the overloaded polling system increases by a deterministic times over times under passage to the fluid dynamics and the fluid limit preserves some randomness. The present paper aims to extend the overloaded asymptotics in Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] to the corresponding polling system with general branching-type service disciplines and customer re-routing policy. A unifying overloaded asymptotic property is derived. Due to the exhaustiveness, the property is a natural extension of the classical polling model with multigated service discipline in Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] and provides new exact results that have not been observed before for rerouting policy. Additionally, a stochastic simulation is undertaken for the validation of the fluid limit and the optimization of the gating indexes to minimize the total population is considered as an example to demonstrate the usefulness of the random fluid limit.

A Bidirectional Polling MAC Mechanism for IoT

The Point Coordination Function (PCF)-based access control mechanism in IEEE 802.11 allows an access point to schedule stations in order to avoid hidden nodes and collisions. However, nearly all existing performance analysis models focus on the single-directional communication scenario, and these polling mechanisms consume a significant amount of energy resources. This study proposes a hybrid service bidirectional polling access control mechanism for transmission between an AP and N stations. To improve energy efficiency, the downlink data queue is assigned after all the uplink station queues, which allows the uplink station to sleep after it completes the data transmission, and it can remain in the sleep state until the downlink begins to broadcast. Then, a classical two-queue asymmetrical polling model is employed to analyze the performance of the PCF-based bidirectional access control system, and a Markov chain and generating function are used to derive a closed-form expression of the mean access delay for the uplink and downlink data. Simulations confirm that the proposed MAC mechanism could provide a maximum energy consumption reduction to 70% for 80 stations with respect to the limited-1 service mechanism in IEEE 802.11a PCF and the two-level polling model. Our analytical results are highly accurate for both homogeneous and heterogeneous traffic.

Two queues with random time-limited polling

TWO QUEUES WITH RANDOM TIME-LIMITED POLLINGIn this paper, we analyse a single server polling model withtwo queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues withgenerally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is noswitch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.