IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Improving Service by Informing Customers About Anticipated Delays

  • Ward Whitt

    (AT&T Labs, Shannon Laboratory, 180 Park Avenue, Florham Park, New Jersey 07932-0971)

Registered author(s):

    This paper investigates the effect upon performance in a service system, such as a telephone call center, of giving waiting customers state information. In particular, the paper studies two M/M/s/r queueing models with balking and reneging. For simplicity, it is assumed that each customer is willing to wait a fixed time before beginning service. However, customers differ, so the delay tolerances for successive customers are random. In particular, it is assumed that the delay tolerance of each customer is zero with probability \beta , and is exponentially distributed with mean \alpha -1 conditional on the delay tolerance being positive. Let N be the number of customers found by an arrival. In Model 1, no state information is provided, so that if N \ge s, the customer balks with probability \beta ; if the customer enters the system, he reneges after an exponentially distributed time with mean \alpha -1 if he has not begun service by that time. In Model 2, if N = s + k \ge s, then the customer is told the system state k and the remaining service times of all customers in the system, so that he balks with probability \beta + (1 - \beta )(1 - q k), where q k = P(T > S k), T is exponentially distributed with mean \alpha -1 , S k is the sum of k + 1 independent exponential random variables each with mean (s\mu ) -1 , and \mu -1 is the mean service time. In Model 2, all reneging is replaced by balking. The number of customers in the system for Model 1 is shown to be larger than that for Model 2 in the likelihood-ratio stochastic ordering. Thus, customers are more likely to be blocked in Model 1 and are more likely to be served without waiting in Model 2. Algorithms are also developed for computing important performance measures in these, and more general, birth-and-death models.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://dx.doi.org/10.1287/mnsc.45.2.192
    Download Restriction: no

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 2 (February)
    Pages: 192-207

    as
    in new window

    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:192-207
    Contact details of provider: Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA
    Phone: +1-443-757-3500
    Fax: 443-757-3515
    Web page: http://www.informs.org/
    Email:


    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:192-207. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.