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Keywords = fixed batch service

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19 pages, 502 KiB  
Article
A Dual Tandem Queue as a Model of a Pick-Up Point with Batch Receipt and Issue of Parcels
by Alexander N. Dudin, Olga S. Dudina, Sergei A. Dudin and Agassi Melikov
Mathematics 2025, 13(3), 488; https://doi.org/10.3390/math13030488 - 31 Jan 2025
Viewed by 788
Abstract
Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for [...] Read more.
Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for accepting orders for delivery. The existence of the time lag between order placing and delivery to the pick-up point is accounted for via modeling the order’s processing as the service in the dual tandem queueing system. Distinguishing features of this tandem queue are the account of possible irregularity in order generation via consideration of the versatile Markov arrival process and the possibilities of batch transfer of the orders to the pick-up point, group withdrawal of orders there, and client no-show. To reduce the probability of an order rejection at the pick-up point due to the overflow of the warehouse, a threshold strategy of order admission at the first stage on a tandem is proposed. Under the fixed value of the threshold, tandem operation is described by the continuous-time multidimensional Markov chain with a block lower Hessenberg structure for the generator. Stationary performance measures of the tandem system are calculated. Numerical results highlight the dependence of these measures on the capacity of the warehouse and the admission threshold. The possibility of the use of the results for managerial goals is demonstrated. In particular, the results can be used for the optimal selection of the capacity of a warehouse and the policy of suspending order admission. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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19 pages, 2501 KiB  
Article
Cost Optimization in Sintering Process on the Basis of Bulk Queueing System with Diverse Services Modes and Vacation
by Subramani Palani Niranjan, Suthanthira Raj Devi Latha and Sorin Vlase
Mathematics 2024, 12(22), 3535; https://doi.org/10.3390/math12223535 - 12 Nov 2024
Cited by 2 | Viewed by 1029
Abstract
This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined [...] Read more.
This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘a’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘a’. When returning from vacation, if threshold ‘a’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost. Full article
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications)
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13 pages, 285 KiB  
Article
Entropy Analysis of a Flexible Markovian Queue with Server Breakdowns
by Messaoud Bounkhel, Lotfi Tadj and Ramdane Hedjar
Entropy 2020, 22(9), 979; https://doi.org/10.3390/e22090979 - 3 Sep 2020
Cited by 1 | Viewed by 2224
Abstract
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue [...] Read more.
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold level c, the server serves customers one a time when the queue length is less than c, and in batches of fixed size c when the queue length is greater than or equal to c. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach. Full article
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
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15 pages, 4363 KiB  
Article
Research of Eliminating the Day-Boundary Discontinuities in GNSS Carrier Phase Time Transfer through Network Processing
by Xiangbo Zhang, Ji Guo, Yonghui Hu, Dangli Zhao and Zaimin He
Sensors 2020, 20(9), 2622; https://doi.org/10.3390/s20092622 - 4 May 2020
Cited by 9 | Viewed by 2735
Abstract
Time and frequency transfer through global navigation satellite system (GNSS) precise point positioning (PPP) based on carrier-phase measurements has been widely used for clock comparisons in national timing laboratories. However, the time jumps up to one nanosecond at the day boundary epochs of [...] Read more.
Time and frequency transfer through global navigation satellite system (GNSS) precise point positioning (PPP) based on carrier-phase measurements has been widely used for clock comparisons in national timing laboratories. However, the time jumps up to one nanosecond at the day boundary epochs of adjacent daily batches lead to discontinuities in the time transfer results. Therefore, it is a major obstacle to achieve continuous carrier phase time transfer. The day-boundary discontinuities have been studied for many years, and they are believed to be caused by the long-term pseudorange noise during estimation of the clock offset in the daily batches and are nearly in accordance with a Gaussian curve. Several methods of eliminating the day-boundary discontinuity were proposed during the past fifteen years, such as shift and overlapping, longer batch processing, clock handover, and ambiguity stacking. Some errors and new noise limit the use of such methods in the long-term clock stability comparison. One of the effective methods is phase ambiguity fixing resolution in zero-differenced PPP, which is based on the precise products of wide-lane satellite bias (WSB) provided by the new international GNSS Service (IGS) Analysis Center of Centre National d’Etudes Spatiales (CNES) and Collecte Localisation Satellites (CLS). However, it is not suitable for new GNSS, such as the Beidou Satellite System (BDS), GALILEO, and QZSS. For overcoming the drawbacks above, Multi-GNSS Experiment (MGEX) observation data of 10 whole days from MJD 58624 to 58633have been network processed by batch least square resolution. These observations come from several ground receivers located in different national timing laboratories. Code and carrier phase ionosphere-free measurements of GPS and BDS satellites are used, and the time transfer results from network processing are compared with PPP results provided by Bureau International des Poids et Mesures (BIPM) and used for international atomic time (TAI) computation (TAIPPP) and universal time coordination (UTC). It is shown that the time offsets of three different time links are almost continuous and the day-boundary discontinuities are sharply eliminated by network processing, although a little extent of day-boundary discontinuities still exist in the results of UTC(USNO)-UTC(PTB). The accuracy of time transfer has been significantly improved, and the frequency stability of UTC(NTSC)-UTC(PTB) can be up to 6.8 × 10−15 on average time of more than one day. Thus, it is suitable for continuous multi-GNSS time transfer, especially for long-term clock stability comparison. Full article
(This article belongs to the Section Remote Sensors)
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7 pages, 224 KiB  
Article
Comparison of Single, Fixed-Time Artificial Insemination in Gilts Using Two Different Protocols to Synchronize Ovulation
by Lima Rodrigues, Rocio Amezcua, Glen Cassar, Terri L O’Sullivan and Robert Friendship
Animals 2020, 10(2), 306; https://doi.org/10.3390/ani10020306 - 14 Feb 2020
Cited by 8 | Viewed by 3435
Abstract
In order to efficiently have a consistent supply of service-ready gilts available to incorporate into each batch of breeding sows, it is necessary to manipulate the timing of estrus and possibly the timing of ovulation of gilts. Estrus can be synchronized by the [...] Read more.
In order to efficiently have a consistent supply of service-ready gilts available to incorporate into each batch of breeding sows, it is necessary to manipulate the timing of estrus and possibly the timing of ovulation of gilts. Estrus can be synchronized by the withdrawal of altrenogest after at least 14 days of treatment. It is possible that protocols developed to induce ovulation, and therefore allow fixed-time artificial insemination (FTAI), can improve the predictability of gilt breeding. This study investigated the effect of two FTAI protocols in gilts on reproductive performance and timing of farrowing and piglet weaning weight compared to gilts bred based on signs of estrus after cessation of altrenogest. Puberty was induced in gilts, followed by treatment with altrenogest. Following altrenogest withdrawal, 180 gilts were assigned to one of three treatment groups. Group 1 gilts (LUT, n = 62) were treated with 600 IU equine chorionic gonadotropin 24 h after altrenogest withdrawal and 5 mg porcine luteinizing hormone (pLH) 80 h later, followed by a single FTAI 36 h after pLH. Group 2 gilts (TRI, n= 61) received 2 mL of a gonadotropin-releasing hormone agonist, triptorelin acetate, intravaginally 6 d after altrenogest withdrawal and were bred by a single FTAI 24 h later. Group 3 gilts (CON, n = 57) were observed for estrus and bred twice by AI, 24 h apart. LUT and TRI gilts farrowed closer together (2.4 ± 1.6 and 2.9 ± 1.2 d(days), respectively) compared to CON gilts (4.5 ± 3.3 d). Piglets in LUT were 80 g (p < 0.001) heavier and piglets in TRI were 64 g (p < 0.05) heavier at weaning than CON piglets, when controlling for birth weight. Results indicate that FTAI might be useful as a means of minimizing the time from the first to the last gilt farrowing in a breeding batch of gilts. However, modifications of the protocols may be required to ensure optimum farrowing rates and litter size. Full article
(This article belongs to the Special Issue Pig Reproduction)
13 pages, 1345 KiB  
Article
Stream Data Load Prediction for Resource Scaling Using Online Support Vector Regression
by Zhigang Hu, Hui Kang and Meiguang Zheng
Algorithms 2019, 12(2), 37; https://doi.org/10.3390/a12020037 - 14 Feb 2019
Cited by 11 | Viewed by 4838
Abstract
A distributed data stream processing system handles real-time, changeable and sudden streaming data load. Its elastic resource allocation has become a fundamental and challenging problem with a fixed strategy that will result in waste of resources or a reduction in QoS (quality of [...] Read more.
A distributed data stream processing system handles real-time, changeable and sudden streaming data load. Its elastic resource allocation has become a fundamental and challenging problem with a fixed strategy that will result in waste of resources or a reduction in QoS (quality of service). Spark Streaming as an emerging system has been developed to process real time stream data analytics by using micro-batch approach. In this paper, first, we propose an improved SVR (support vector regression) based stream data load prediction scheme. Then, we design a spark-based maximum sustainable throughput of time window (MSTW) performance model to find the optimized number of virtual machines. Finally, we present a resource scaling algorithm TWRES (time window resource elasticity scaling algorithm) with MSTW constraint and streaming data load prediction. The evaluation results show that TWRES could improve resource utilization and mitigate SLA (service level agreement) violation. Full article
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