Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone
Travel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way trave...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-07-01
|
| Series: | Logistics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2305-6290/3/3/17 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839602069526282240 |
|---|---|
| author | Todor Todorov |
| author_facet | Todor Todorov |
| author_sort | Todor Todorov |
| collection | DOAJ |
| description | Travel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way travel from a random to another random location. The probability density function (PDF) of the travelling time for a semi-random trip in a one-dimensional zone is expressed analytically for all possible locations of its starting point. The PDF of a random trip within the same zone is found as a marginal probability by considering all possible durations for such travel. Then the PDFs for the travel times of single command (SC) and dual command (DC) cycles are obtained by scaling the PDF for the travel time of a semi-random trip (for SC) and as the maximum travel time of two independent semi-random trips (for DC). PDFs for travel times in a two-dimensional service zone with taxicab geometry are calculated by considering the trip as a superposition of two one-dimensional trips. The PDFs for travel times of SC and DC cycles are calculated in the same way. Both the one-dimensional and the two-dimensional service zones are analyzed in the time domain without normalization. The PDFs for all travel times are expressed in an analytical form parameterized by the maximal possible travel time within the zone. The graphs of all PDFs are illustrated by numerical examples. |
| format | Article |
| id | doaj-art-5def637393b54b3b99e67874b1045abf |
| institution | Matheson Library |
| issn | 2305-6290 |
| language | English |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Logistics |
| spelling | doaj-art-5def637393b54b3b99e67874b1045abf2025-08-02T09:01:58ZengMDPI AGLogistics2305-62902019-07-01331710.3390/logistics3030017logistics3030017Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the ZoneTodor Todorov0Faculty of Mechanical Engineering, Technical University of Sofia, 8 Kliment Ohridski Boulevard, 1000 Sofia, BulgariaTravel times for simple trips and cycles are analyzed for a storage/retrieval machine working in a one-dimensional or two-dimensional zone with taxicab geometry. A semi-random trip is defined as one-way travel from a known to a random location or vice versa. A random trip is defined as one-way travel from a random to another random location. The probability density function (PDF) of the travelling time for a semi-random trip in a one-dimensional zone is expressed analytically for all possible locations of its starting point. The PDF of a random trip within the same zone is found as a marginal probability by considering all possible durations for such travel. Then the PDFs for the travel times of single command (SC) and dual command (DC) cycles are obtained by scaling the PDF for the travel time of a semi-random trip (for SC) and as the maximum travel time of two independent semi-random trips (for DC). PDFs for travel times in a two-dimensional service zone with taxicab geometry are calculated by considering the trip as a superposition of two one-dimensional trips. The PDFs for travel times of SC and DC cycles are calculated in the same way. Both the one-dimensional and the two-dimensional service zones are analyzed in the time domain without normalization. The PDFs for all travel times are expressed in an analytical form parameterized by the maximal possible travel time within the zone. The graphs of all PDFs are illustrated by numerical examples.https://www.mdpi.com/2305-6290/3/3/17probability density functiontravel timeone dimensiontaxicab geometryManhattan distancetaxicab geometrysingle commanddual command |
| spellingShingle | Todor Todorov Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone Logistics probability density function travel time one dimension taxicab geometry Manhattan distance taxicab geometry single command dual command |
| title | Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone |
| title_full | Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone |
| title_fullStr | Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone |
| title_full_unstemmed | Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone |
| title_short | Probability Density Functions for Travel Times in One-Dimensional and Taxicab Service Zones Parameterized by the Maximal Travel Duration of the S/R Machine Within the Zone |
| title_sort | probability density functions for travel times in one dimensional and taxicab service zones parameterized by the maximal travel duration of the s r machine within the zone |
| topic | probability density function travel time one dimension taxicab geometry Manhattan distance taxicab geometry single command dual command |
| url | https://www.mdpi.com/2305-6290/3/3/17 |
| work_keys_str_mv | AT todortodorov probabilitydensityfunctionsfortraveltimesinonedimensionalandtaxicabservicezonesparameterizedbythemaximaltraveldurationofthesrmachinewithinthezone |