{"id":2115,"date":"2005-01-16T11:15:14","date_gmt":"2005-01-16T16:15:14","guid":{"rendered":"https:\/\/engineering.jhu.edu\/magazine-archive\/?p=2115"},"modified":"2014-12-16T11:16:31","modified_gmt":"2014-12-16T16:16:31","slug":"stuck-traffic-heres","status":"publish","type":"post","link":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/","title":{"rendered":"Stuck in Traffic? Here\u2019s Why."},"content":{"rendered":"<figure id=\"attachment_2116\" class=\"wp-caption alignleft\" style=\"width: 136px\"><a href=\"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2116\" src=\"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg\" alt=\"In his brief career, Mathematical Sciences alumnus Alvin Lim \u201902 PhD has already found that, for starters, the models known as MPECs can help ease traffic jams, improve the bottom line for airlines, and get the most bang for the buck from a limited marketing budget.\" width=\"126\" height=\"184\" \/><\/a><figcaption class=\"wp-caption-text\"><strong>In his brief career, Mathematical Sciences alumnus Alvin Lim \u201902 PhD has already found that, for starters, the models known as MPECs can help ease traffic jams, improve the bottom line for airlines, and get the most bang for the buck from a limited marketing budget.<\/strong><\/figcaption><\/figure>\n<p>When Alvin Lim \u201902 PhD looks at any problem that involves optimization\u2014whether it\u2019s traffic flow, airline revenues, or grocery prices\u2014he sees something called a Mathema- tical Program with Equilibrium Constraints (MPEC).<\/p>\n<p>MPECs, pioneered by Jong-Shi Pang, former Whiting School of Engineering professor of Mathematical Sciences (now Applied Mathematics and Statistics), offer a model for maximizing the use of resources while addressing the often conflicting goals of planners and users. While studying with Pang, an expert in operations research and MPECs, Lim became interested in the application of MPECs. Pang had three PhD students working in MPEC problems, Lim recalls, \u201cone in finance, another in power distribution, and me in transportation science. The three of us were learning the same math concepts but applying them to completely different fields.\u201d<\/p>\n<p>The wide-ranging implications of MPECs, plus Lim\u2019s understanding of how they can be applied, were recognized when his dissertation, \u201cTransportation Network Design Problems: An MPEC Approach,\u201d received an award from the 2002 Transportation Science Section Dissertation Prize Committee of the Institute for Operations Research and the Management Sciences (INFORMS). Lim\u2019s research involved optimization of the design of transportation networks by explicitly including user equilibrium behavior in the constraints. \u201cWhat prevents people from solving transportation engineering problems is the difficulty of designing an efficient road network capable of accounting for a natural tendency toward inefficient use,\u201d he explains.<\/p>\n<p>Consider this conundrum: to a traffic planner, the \u201cbest\u201d road network is one that is used maximally, and this is how most road networks should be planned. But to a driver, the only system that matters is finding the \u201cbest\u201d way from point A to point B. \u201cBest\u201d can mean different things. One person may want to travel quickly; another may prefer a scenic route. The same driver may want to do both at different times, and so on. When a large group of drivers subscribes to the same goal, traffic congestion occurs. This leads to a non-optimal use of the road network due to unbalanced load of the roads. So, drivers\u2019 natural behavior results in inefficient use of the network.<\/p>\n<p>Drivers tend to behave in such a way that only the \u201cbest\u201d routes will have traffic flows\u2014a state known as user equilibrium. Ideally, says Lim, planners \u201cshould solve their optimization problems based on this \u2018selfish\u2019 behavior of drivers.\u201d This is, he says, a \u201cbi-level optimization\u201d problem. \u201cIt is difficult to model and solve problems where the conflicting goals of the planners and the users are both taken into account,\u201d he says. \u201cThere is no software to solve this.\u201d However, in his dissertation, Lim studied existing ways of forcing more efficient use of the road 2005network, such as setting tolls or adjusting timing of traffic lights. He also proposed possible solutions to resulting MPEC optimization problems by applying the appropriate algorithms.<\/p>\n<p>The power of MPECs are not limited to solving traffic congestion. While he was senior operations research specialist at Delta Technology, a wholly owned subsidiary of Delta Air Lines, Lim applied the MPEC approach to solving the airline passenger optimal overbooking problem and an airline version of the origin-destination demand estimation problem. Like traffic planners, airlines must calculate loads on their airplanes and plan routes accordingly. Once again, consumer behavior bedevils their efforts.<\/p>\n<p>\u201cWhat airlines do is forecast how many passengers will be there for each flight,\u201d Lim says. \u201cUnfortunately, a consumer does not buy tickets this way; he is interested only in getting from his origin to his destination, which typically requires more than one flight.\u201d It is easy for the airline to collect information at flight level and make predictions based on this data. But it is difficult to predict an individual traveler\u2019s origination and destination. \u201cWe are attempting to understand scheduling more in terms of how passengers behave,\u201d Lim explains.<\/p>\n<p>In his current position as optimization consultant at Marketing Analytics in Evanston, Illinois, Lim applies these same optimization concepts to helping clients achieve their marketing goals. For example, he says, \u201ca dominant company, such as Wal-Mart, sets promotional pricing for certain categories of products\u201d and \u201cneeds to maximize their sales or profit in anticipation of the pricing the competition might set.\u201d He also helps clients allocate their marketing budget to achieve the best return on investment.<\/p>\n<p>A native of the Philippines, Lim recalls, \u201cI would see these incredible traffic problems in crowded cities and wonder: \u2018Why doesn\u2019t it ever help when the government tries to improve traffic? When I came to Hopkins and started applying MPEC to these problems, I began to understand. In certain situations, adding more roads without carefully studying the underlying problem may actually worsen the congestion problems. Now, in my new position, I am shifting gears again, and that is a challenge. But it is all still within the realm of mathematical optimization. That\u2019s the nice thing about mathematical modeling,\u201d he says. \u201cThat is what makes it so beautiful.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When Alvin Lim \u201902 PhD looks at any problem that involves optimization\u2014whether it\u2019s traffic flow, airline revenues, or grocery prices\u2014he sees something called a Mathema- tical Program with Equilibrium Constraints (MPEC). MPECs, pioneered by Jong-Shi Pang, former Whiting School of Engineering professor of Mathematical Sciences (now Applied Mathematics and Statistics), offer a model for maximizing&#8230;<\/p>\n","protected":false},"author":4,"featured_media":2116,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[78],"tags":[],"class_list":["post-2115","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-alumni-legacy","issue-winter-2005"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine\" \/>\n<meta property=\"og:description\" content=\"When Alvin Lim \u201902 PhD looks at any problem that involves optimization\u2014whether it\u2019s traffic flow, airline revenues, or grocery prices\u2014he sees something called a Mathema- tical Program with Equilibrium Constraints (MPEC). MPECs, pioneered by Jong-Shi Pang, former Whiting School of Engineering professor of Mathematical Sciences (now Applied Mathematics and Statistics), offer a model for maximizing...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/\" \/>\n<meta property=\"og:site_name\" content=\"JHU Engineering Magazine\" \/>\n<meta property=\"article:published_time\" content=\"2005-01-16T16:15:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2014-12-16T16:16:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"126\" \/>\n\t<meta property=\"og:image:height\" content=\"184\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Abby Lattes\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Abby Lattes\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"NewsArticle\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/\"},\"author\":{\"name\":\"Abby Lattes\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/#\\\/schema\\\/person\\\/0244393be370fbc3ead8ec26062e9742\"},\"headline\":\"Stuck in Traffic? Here\u2019s Why.\",\"datePublished\":\"2005-01-16T16:15:14+00:00\",\"dateModified\":\"2014-12-16T16:16:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/\"},\"wordCount\":877,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/wp-content\\\/uploads\\\/2014\\\/07\\\/4_5004.jpg\",\"articleSection\":[\"Alumni up front\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/\",\"name\":\"Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/wp-content\\\/uploads\\\/2014\\\/07\\\/4_5004.jpg\",\"datePublished\":\"2005-01-16T16:15:14+00:00\",\"dateModified\":\"2014-12-16T16:16:31+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/#\\\/schema\\\/person\\\/0244393be370fbc3ead8ec26062e9742\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#primaryimage\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/wp-content\\\/uploads\\\/2014\\\/07\\\/4_5004.jpg\",\"contentUrl\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/wp-content\\\/uploads\\\/2014\\\/07\\\/4_5004.jpg\",\"width\":126,\"height\":184,\"caption\":\"In his brief career, Mathematical Sciences alumnus Alvin Lim \u201902 PhD has already found that, for starters, the models known as MPECs can help ease traffic jams, improve the bottom line for airlines, and get the most bang for the buck from a limited marketing budget.\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/2005\\\/01\\\/stuck-traffic-heres\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Stuck in Traffic? Here\u2019s Why.\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/#website\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/\",\"name\":\"JHU Engineering Magazine\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/magazine-archive\\\/#\\\/schema\\\/person\\\/0244393be370fbc3ead8ec26062e9742\",\"name\":\"Abby Lattes\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g\",\"caption\":\"Abby Lattes\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/","og_locale":"en_US","og_type":"article","og_title":"Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine","og_description":"When Alvin Lim \u201902 PhD looks at any problem that involves optimization\u2014whether it\u2019s traffic flow, airline revenues, or grocery prices\u2014he sees something called a Mathema- tical Program with Equilibrium Constraints (MPEC). MPECs, pioneered by Jong-Shi Pang, former Whiting School of Engineering professor of Mathematical Sciences (now Applied Mathematics and Statistics), offer a model for maximizing...","og_url":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/","og_site_name":"JHU Engineering Magazine","article_published_time":"2005-01-16T16:15:14+00:00","article_modified_time":"2014-12-16T16:16:31+00:00","og_image":[{"width":126,"height":184,"url":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg","type":"image\/jpeg"}],"author":"Abby Lattes","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Abby Lattes","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"NewsArticle","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#article","isPartOf":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/"},"author":{"name":"Abby Lattes","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/#\/schema\/person\/0244393be370fbc3ead8ec26062e9742"},"headline":"Stuck in Traffic? Here\u2019s Why.","datePublished":"2005-01-16T16:15:14+00:00","dateModified":"2014-12-16T16:16:31+00:00","mainEntityOfPage":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/"},"wordCount":877,"commentCount":0,"image":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#primaryimage"},"thumbnailUrl":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg","articleSection":["Alumni up front"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/","url":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/","name":"Stuck in Traffic? Here\u2019s Why. - JHU Engineering Magazine","isPartOf":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/#website"},"primaryImageOfPage":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#primaryimage"},"image":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#primaryimage"},"thumbnailUrl":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg","datePublished":"2005-01-16T16:15:14+00:00","dateModified":"2014-12-16T16:16:31+00:00","author":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/#\/schema\/person\/0244393be370fbc3ead8ec26062e9742"},"breadcrumb":{"@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#primaryimage","url":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg","contentUrl":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-content\/uploads\/2014\/07\/4_5004.jpg","width":126,"height":184,"caption":"In his brief career, Mathematical Sciences alumnus Alvin Lim \u201902 PhD has already found that, for starters, the models known as MPECs can help ease traffic jams, improve the bottom line for airlines, and get the most bang for the buck from a limited marketing budget."},{"@type":"BreadcrumbList","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/2005\/01\/stuck-traffic-heres\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/engineering.jhu.edu\/magazine-archive\/"},{"@type":"ListItem","position":2,"name":"Stuck in Traffic? Here\u2019s Why."}]},{"@type":"WebSite","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/#website","url":"https:\/\/engineering.jhu.edu\/magazine-archive\/","name":"JHU Engineering Magazine","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/engineering.jhu.edu\/magazine-archive\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/engineering.jhu.edu\/magazine-archive\/#\/schema\/person\/0244393be370fbc3ead8ec26062e9742","name":"Abby Lattes","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c56cb7af5427f847aa288542444ba9ff3d2107bf85dc6c6d44a4d1315608258d?s=96&r=g","caption":"Abby Lattes"}}]}},"_links":{"self":[{"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/posts\/2115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/comments?post=2115"}],"version-history":[{"count":2,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/posts\/2115\/revisions"}],"predecessor-version":[{"id":2808,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/posts\/2115\/revisions\/2808"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/media\/2116"}],"wp:attachment":[{"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/media?parent=2115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/categories?post=2115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/engineering.jhu.edu\/magazine-archive\/wp-json\/wp\/v2\/tags?post=2115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}