Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative real-time delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delay-history estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multi-server queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the many-server and classical heavy-traffic limiting regimes.

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We consider tandem lines with finite buffers and flexible, heterogeneous servers who are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should be assigned dynamically to tasks in order to maximize the long-run average throughput. In particular, we investigate when it is better to take advantage of synergy among servers, rather than exploiting the servers ’ special skills, to achieve the best possible system throughput. For Markovian systems with two stations and two servers, we provide a complete characterization of the optimal policy and show that depending on how well the servers work together, the optimal policy either takes full advantage of servers ’ special skills, or full advantage of server synergy (and hence there is no middle ground in this case). Moreover, for a class of Markovian systems, we provide sufficient conditions that guarantee that the optimal policy should take full advantage of server synergy at all times. Finally, we show that when there is no tradeoff between server synergy and servers ’ special skills (because the servers are generalists who are equally skilled at all tasks), the optimal policy has servers working in teams of two or more at all times. 1

First call resolution, which in essence means the proportion of inquires that are successfully addressed after one call (note that the definitions of FCR differ, see below), has been getting more attention in call center management. A review of the literature, however, reveals that most of the interest has come from the practitioners (call center managers, consultants, etc.). We can only find a few research reports on FCR- the benefits, the potential downsides, and more importantly, how FCR should be implemented in the routing of calls. 1

A fundamental aspect of designing queueing systems with stationary servers is identifying and improving the system bottlenecks. In this paper, the concept of a bottleneck is extended to queueing networks with heterogeneous, flexible servers. In contrast with a network with stationary servers, the bottlenecks are not a priori obvious, but can be determined by solving a number of linear programming problems. Unlike the stationary server case, we find that a bottleneck may span several queues. We then identify some characteristics of desirable flexibility structures. In particular, the chosen flexibility structure should not only achieve the maximal possible capacity (corresponding to full server flexibility), but should also have the feature that the entire network is the (unique) system bottleneck. The reason is that it is then possible to shift capacity between arbitrary points in the network, allowing the network to cope with demand fluctuations. Finally, we discuss how knowledge of the system bottleneck may be used to decide how to add server flexibility to an existing network. 1

In many call centers, agents are trained to handle all arriving calls but exhibit very different performance for the same call type, where performance is defined by the average call handling time (AHT) and the call resolution probability (RP). In this paper, we explore strategies for determining which calls should be handled by which agents, where these assignments are dynamically determined based on the specific attributes of the agents and/or the current state of the system. We test several routing strategies using data obtained from a large financial service firm’s customer service call centers and present empirical performance results. These results allow us to characterize overall performance in terms of customer waiting time and overall resolution rate, identifying an efficient frontier of routing rules for this contact center. 1

Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in many-server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time-varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant estimation bias in delayhistory-based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay-history estimators that effectively cope with time-varying arrival rates together with non-exponential service-time and abandonment-time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.

Motivated by interest in making delay announcements in service systems, we develop new real-time delay predictors that effectively cope with customer abandonment and time-varying parameters. First, we focus on delay predictors exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant prediction bias in delay-history-based predictors when the system experiences alternating periods of overload and underload. We then introduce a new delay-history-based predictor that effectively copes with time-varying arrival rates. Second, we consider a time-varying number of servers. We develop two new predictors which exploit an established deterministic fluid approximation for a many-server queueing model with time-varying demand and capacity. The new predictors effectively cope with those features, often observed in practice. Throughout, we use computer simulation to quantify the performance of the alternative delay predictors. 1

Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in many-server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time-varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant estimation bias in delayhistory-based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay-history estimators that effectively cope with time-varying arrival rates together with non-exponential service-time and abandonment-time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.

Consider a Markovian system of two stations in tandem with finite intermediate buffer and two servers. The servers are heterogeneous, flexible, and more efficient when they work on their own than when they collaborate. We determine how the servers should be assigned dynamically to the stations with the goal of maximizing the system throughput. We show that the optimal policy depends on whether or not one server is dominant (i.e., faster at both stations) and on the magnitude of the efficiency loss of collaborating servers. In particular, if one server is dominant then he must divide his time between the two stations and we identify the threshold policy the dominant server should use; otherwise each server should focus on the station where he is the faster server. In all cases, servers only collaborate to avoid idleness when the first station is blocked or the second station is starved, and we determine when collaboration is preferable to idleness as a function of the efficiency loss of collaborating servers. 1