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

Todor Todorov
Additional contact information
Todor Todorov: Faculty of Mechanical Engineering, Technical University of Sofia, 8 Kliment Ohridski Boulevard, 1000 Sofia, Bulgaria

Logistics, 2019, vol. 3, issue 3, 1-15

Abstract: 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.

Keywords: probability density function; travel time; one dimension; taxicab geometry; Manhattan distance; taxicab geometry; single command; dual command (search for similar items in EconPapers)
JEL-codes: L8 L80 L81 L86 L87 L9 L90 L91 L92 L93 L98 L99 M1 M10 M11 M16 M19 R4 R40 R41 R49 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2305-6290/3/3/17/pdf (application/pdf)
https://www.mdpi.com/2305-6290/3/3/17/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jlogis:v:3:y:2019:i:3:p:17-:d:244977

Access Statistics for this article

Logistics is currently edited by Ms. Mavis Li

More articles in Logistics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().