Busy Period Research Articles

Navigating the busy exam period

Young Vet Network representative and small animal vet Alice Moore offers some advice for vet students heading into the exam season.

Cost optimization of single server retrial queueing model with Bernoulli schedule working vacation, vacation interruption and balking

In present paper an M/M/1 retrial queueing model with working vacation interruption using Bernoulli schedule and Balking is analyzed under classical retrial policy. When sever is occupied in regular busy period customer enters in system with probability b and during working vacation of server, customer joins the orbit with probability v. Whenever no customers are in the system after vacation completion then either server returns to normal free state with probability q or goes for multiple working vacation with probability 1-q. Server provides the service at lower rate during working vacation than normal busy period. In this paper steady state probabilities have been obtained using probability generating function technique. Some important performance measures of this model are also evaluated numerically and some results are shown graphically using MATLAB software.

Frequency scaling in multilevel queues

In this paper, we study a variant of PS+PS multilevel scheduling, which we call the PS+IS queue. Specifically, we use Processor Sharing (PS) at both queues, but with linear frequency scaling on the second queue, so that the latter behaves like an Infinite Server (IS) queue. The goals of the system are low response times for small jobs in the first queue, and reduced power consumption for large jobs in the second queue. The novelty of our model includes the frequency scaling at the second queue, and the batch arrival process at the second queue induced by the busy period structure of the first queue which has strictly higher priority. We derive a numerical solution for the PS+IS queueing system in steady-state, and then study its properties under workloads obtained from fitting of TCP flow traces. The simulation results confirm the e

An Uncertain Single-Server Queueing Model

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

A busy period approach to some queueing games

The traditional approach when looking for a symmetric equilibrium behavior in queueing models with strategic customers who arrive according to some stationary arrival process is to look for a strategy which, if used by all, is also a best response of an individual customer under the resulting stochastic steady-state conditions. This description lacks a key component: a proper definition of the set of players. Hence, many of these models cannot be defined as proper noncooperative games. This limitation raises two main concerns. First, it is hard to formulate these models in a canonical way, and hence, results are typically limited to a specific model or to a narrow class of models. Second, game theoretic results cannot be applied directly in the analysis of such models and call for ad hoc adaptations. We suggest a different approach, one that is based on the stationarity of the underlying stochastic processes. In particular, instead of considering a system that is functioning from time immemorial and has already reached stochastic steady-state conditions, we look at the process as a series of isolated, a priori identical, and independent strategic situations with a random, yet finite, set of players. Each of the isolated games can be analyzed using existing tools from the classical game theoretic literature. Moreover, this approach suggests a canonic definition of strategic queueing models as properly defined mathematical objects. A significant advantage of our approach is its compatibility with models in the existing literature. This is exemplified in detail for the famous model of the unobservable “to queue or not to queue” problem and other related models.

A discrete-time queueing system with three different strategies

We consider a discrete-time Geo/G/1/∞ system in which a customer that finishes its first essential service may opt to abandon the system, to receive a second optional service or to go at the head of the queue in order to receive another essential service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Using a generating function approach the distribution of the number of customers in the queue and in the system as well as their respective means are given.The busy period of an auxiliary system, that will be useful to study of the customers delay, is analysed. The distributions of the sojourn time of a customer in the server, the queue and the system are provided. In order to illustrate the effect of the parameters on several performance characteristics some numerical examples are given. Finally, a section of conclusions commenting the main research contributions of this paper is presented.

Working conditions and labor flexibility in non-family farms: weather-based labor management by Japanese paddy rice corporations

Improving working conditions in agriculture is of great concern throughout the world. Just as in other industries, many young farm workers prefer to work as salaried employees, which has brought attention to non-family farms as providers of employment opportunities. However, in the presence of a strong need to flexibly respond to weather, there is still difficulty regarding whether workplaces without overworking can exist. This study is based on in-depth surveys of non-family rice farms in Fukui Prefecture, Japan. Our findings suggest that even in non-family farms, holiday-setting is done flexibly to account for weather, and systems that allow for harvesting at appropriate times are in place. During the busy farming period, in joint-stock farms, where multiple farmers invest together, full-time employees work overtime. In contrast, in community farms, many community residents take turns for working, which allows work to be done on time. A closer analysis of work records shows that, in either organizational structure, specific members need to overwork. Reasons behind this include issues with sunk costs in the form of monthly wages, lack of skills among part-time employees, and the communication costs of coordinating with many part-time employees.

Evaluation of Total Armada Transport City Route 05B in Cianjur City

The transportation problem is a classic problem that occurs in almost every city in Indonesia, including the city of Cianjur which is located in the province of West Java. One focus of transportation problems in the city of Cianjur is about the number of Cianjur city transportation that is too much operating but not balanced with the number of passengers served. This condition causes the city transportation drivers to fight over passengers to catch up with deposits. The method of conducting the research was carried out by a dynamic survey, carried out in a vehicle by the method of recording the number of passengers who boarded and alighted vehicles traveling on a route, where the officer recorded the number of passengers who boarded and descended and or travel time in each segment. After analyzing, the loading factor value for rush hour and rush hour turns out to be under 50%. The average number of fleets 05B needed to be based on circulation time (K) at morning rush hour 1 unit vehicle/hour, rush hour afternoon 2 units vehicles/hour, and during the afternoon no rush hour 1 unit of vehicle/hour. While the number of trips (fleet trips) needed in the busy period and non-busy time (K ’) in the morning rush hour 2 vehicle trips (trip) / hour, rush hour noon 2 Vehicle trip (trip) / hour and at no-rush hour afternoon 2 Vehicle trip (trip) / hour.

Feasibility and efficiency of agricultural machinery maintenance

The greatest impact on machine uptime and performance is the timely and high-quality maintenance. The main contradiction is inherent in the system of maintenance and use of machines, in the coincidence of the timing of their performance: the more time is spent, the more maintenance operations need to be performed. As a result, during busy periods of fieldwork, to ensure high operating time, to the detriment of prevention, the mechanic has to virtually eliminate only the consequences of failures, which leads to their increase, machine productivity is reduced and operating costs increase. With the current trend of having more than one machine per operator, the operator is physically unable to perform all types of maintenance and repair work alone. Therefore, it would be advisable to transfer some of these works to specialized enterprises. The problem of increasing the reliability of tractors can also be solved by deeper specialization and intensification of maintenance operations during their transfer to nonstressed periods of fieldwork. In the work the structure of formation of technical service at the enterprises of agroindustrial complex is proposed and theoretically grounded. The main advantages of the proposed system of technical service are considered.

Performance Analysis of Multi-processor Two-Stage Tandem Call Center Retrial Queues with Non-Reliable Processors

We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary distribution of the number of calls in the system, the mean number of calls in the orbit, the mean waiting time of calls in the orbit and the mean busy period of the system along with other descriptors of the system are determined by using the matrix-analytic techniques. Besides, the availability analysis of the processors is also studied. Further, we have also discussed the characteristics of the first-passage time to reach the orbit critical level, the number of calls served in the call center during this period and their corresponding moments. Finally, extensive numerical results are presented to highlight the impact of the system parameters on the performance measures of the two-stage tandem call center retrial queueing system under investigation.

Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.

PBN-Based Time-Optimal Terminal Air Traffic Control Using Cellular Automata

Over the last decade, there has been an increase in air transportation, which has raised awareness to provide necessary procedures to respond to air transportation demands and reduce delay costs. One such procedure, “performance-based navigation (PBN),” currently studied, is expected to increase the airspace capacity based on aircraft's individual performances. This research describes an efficient and expandable model for allocating standard terminal arrival route during continuous descent approach (CDA) that effectively uses PBN requirements. As a case study, we have considered the “Atlanta International Airport” and verified the model's accuracy using real-time traffic data. The model is then used to study mixed traffic behavior concerning each aircraft's navigation capability. We show that our technique helps decrease time separation minima, reducing traffic delays by up to 50% during busy periods. Furthermore, we show that our approach could enhance target traffic flow by as much as 25% while maintaining proper separation minima. Finally, we show that near-optimal control advisory could also be obtained to minimize the target traffic flow's total delay.

Busy Season and Proxy Recommendations

The short period of time, from the fourth week of April to the end of May, referred to as the proxy season, has about 333 proposals voted a day relative to 27 proposals voted per day outside the proxy season. The compressed workload results in 17.6% fewer negative recommendations from ISS during this busy period. The proxy season also entails busy voting schedules for institutional investors who in the aggregate, respond by increasing their reliance on ISS recommendations. Aggregate support for proposals with a negative recommendation from ISS is 10% lower during the busy period. Stock price reaction to outcomes in close votes show that successful negative recommendations during the busy period, that is when negative proposals fail, are not value enhancing. In sum, ISS recommendations during busy voting periods are less likely to be negative, have greater influence on voting, and are not value enhancing. The results inform the policy debate on the role and influence of proxy advisors.

Laplace transforms of improper random variables

The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in certain special cases.

Modeling and Predictability Analysis on Channel Spectrum Status Over Heavy Wireless LAN Traffic Environment

Using the real wireless spectrum occupancy status in 2.4 and 5 GHz bands collected at a railway station as representative of a heavy wireless LAN (WLAN) traffic environment, this paper studies the modeling of durations of busy/idle (B/I) status and its predictability based on predictability theory. We first measure and model the channel status in the heavy traffic environment over almost all of the WLAN channels at 2.4 GHz and 5 GHz bands in a busy (rush hour) period and non-busy period. Then, using two selected channels at 2.4 GHz and 5 GHz bands, we analyze the upper bound (UB) and lower bound (LB) of predictability of the busy/idle durations based on predictability theory. The analysis shows that the LB predictability of durations can be easily increased by changing their probability distribution. Based on this property, we introduce the data categorization (DC) method. By categorizing the busy/idle durations into different streams, the proposed data categorization can improve the prediction performance of some streams with large LB predictability, even if it employs a simple low-complexity auto-regressive (AR) predictor.

Transient behaviour of a Markovian vacation queue with re-service balking control of admission closedown and setup times

This paper studies an M/M/1 queueing model with single as well as multiple vacation, closedown, setup times, re-service, balking and control of admission. All the arriving customers are not allowed to join the queue all the time. They are either permitted to join the queue or rejected. Whenever the system becomes empty and the server resumes closedown work. If any customer joins the queue before the completion of closedown, the closedown work is interrupted and the server commences an exhaustive busy period. Otherwise, it starts the vacation after the completion of closedown period. During the vacation period, the permitted arrivals may join the queue or balk. At the moment of completion of vacation, the server begins the setup work before the commencement of service. After the service, each customer has the option to get immediate re-service. The transient and stationary system size probabilities are derived. The time-dependent mean and variance are also obtained. Numerical simulations are also presented.

The analysis of the FM/FM/1 queue with single working vacation and impatience of customers

This paper deals with an M/M/1 queueing system with a single working vacation and reneging of impatient customers and fuzzy parameters. For this fuzzy queueing model, researches fetch performance measure of interest such as the mean number of customer in the system during working vacation, the mean number of customers in the system during regular busy period and the mean of reneging rate of the system. Finally numerical results are presented to show the effects of system parameter.

Variant working vacation Markovian queue with second optional service, unreliable server and retention of reneged customers

In this paper, a variant working vacation queueing system with second optional service, unreliable server, and retention of reneged customers is studied. This model has potential applications in tele-services, banks, manufacturing processes, etc. The expressions of the steady-state probabilities and the system sizes when the server is in different states are obtained using probability generating functions. This paper also discusses an optimisation problem under a given cost structure. Direct search method and quadratic fit search method (QFSM) are applied to obtain the optimum number of working vacations and optimum service rates during regular busy period and working vacation period, respectively.

Analysis of state dependent M[X]/G(a, b)/1 queue with multiple vacation second optional service and optional re-service

The objective of this paper is to analyse an M[X]/G(a, b)/1 queueing model with second optional service, multiple vacation, state dependent arrival and optional re-service. After completing the first essential service, a batch of customers either requests for re-service or leaves the system without re-service. After the completion of first essential service (with or without re-service), the batch of customers either requests for second optional service or leaves the system. At the completion moment of second optional service, the batch of customers either requests for re-service or leaves the system after the second service. Whenever the queue size is less than 'a', the server commences vacation. At the instant of vacation completion, if at least 'a' customers wait for service, the server starts a busy period. Otherwise, the server resumes another vacation. Using supplementary variable technique, the steady-state probability generating function (PGF) of the queue size is obtained.

Analysis of a Variant Working Vacation Queue with Customer Impatience and Server Breakdowns

This paper analyses an infinite buffer single server variant working vacation queueing model in which the arriving customer may balk and the server is subject to breakdown. The service times during regular busy period and working vacation period, vacation times, breakdown times and repair times are assumed to be exponentially distributed and are mutually independent. In working vacation period, the customer may renege due to impatience. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size. In addition, we obtain some performance measures and a total expected profit function per unit time is designed to determine the optimal values at the maximum profit. We employ the particle swarm optimisation method to solve the profit optimisation problem.