Coping with Time-Varying Demand When Setting Staffing Requirements for a Service System

We review queueing-theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long-run steady-state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time-dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time-lag refinements can improve traditional stationary independent period-by-period and peak-hour approximations. Time-varying infinite-server models help develop refinements, because closed-form expressions exist for their time-dependent behavior. More difficult cases with very long service times and other complicated features, such as end-of-day effects, can often be treated by a modified-offered-load approximation, which is based on an associated infinite-server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned

A role of the Nse4 kleisin and Nse1/Nse3 KITE subunits in the ATPase cycle of SMC5/6

The SMC (Structural Maintenance of Chromosomes) complexes are composed of SMC dimers, kleisin and kleisin-interacting (HAWK or KITE) subunits. Mutual interactions of these subunits constitute the basal architecture of the SMC complexes. In addition, binding of ATP molecules to the SMC subunits and their hydrolysis drive dynamics of these complexes. Here, we developed new systems to follow the interactions between SMC5/6 subunits and the relative stability of the complex. First, we show that the N-terminal domain of the Nse4 kleisin molecule binds to the SMC6 neck and bridges it to the SMC5 head. Second, binding of the Nse1 and Nse3 KITE proteins to the Nse4 linker increased stability of the ATP-free SMC5/6 complex. In contrast, binding of ATP to SMC5/6 containing KITE subunits significantly decreased its stability. Elongation of the Nse4 linker partially suppressed instability of the ATP-bound complex, suggesting that the binding of the KITE proteins to the Nse4 linker constrains its limited size. Our data suggest that the KITE proteins may shape the Nse4 linker to fit the ATP-free complex optimally and to facilitate opening of the complex upon ATP binding. This mechanism suggests an important role of the KITE subunits in the dynamics of the SMC5/6 complexes

The melanoma-associated antigen 1 (MAGEA1) protein stimulates the E3 ubiquitin-ligase activity of TRIM31 within a TRIM31-MAGEA1-NSE4 complex

The MAGE (Melanoma-associated antigen) protein family members are structurally related to each other by a MAGEhomology domain comprised of 2 winged helix motifs WH/A and WH/B. This family specifically evolved in placental mammals although single homologs designated NSE3 (non-SMC element) exist in most eukaryotes. NSE3, together with its partner proteins NSE1 and NSE4 form a tight subcomplex of the structural maintenance of chromosomes SMC5–6 complex. Previously, we showed that interactions of the WH/B motif of the MAGE proteins with their NSE4/EID partners are evolutionarily conserved (including the MAGEA1-NSE4 interaction). In contrast, the interaction of the WH/A motif of NSE3 with NSE1 diverged in the MAGE paralogs. We hypothesized that the MAGE paralogs acquired new RING-finger containing partners through their evolution and form MAGE complexes reminiscent of NSE1-NSE3-NSE4 trimers. In this work, we employed the yeast 2-hybrid system to screen a human RING-finger protein library against several MAGE baits. We identified a number of potential MAGE-RING interactions and confirmed several of them (MDM4, PCGF6, RNF166, TRAF6, TRIM8, TRIM31, TRIM41) in co-immunoprecipitation experiments. Among these MAGE-RING pairs, we chose to examine MAGEA1-TRIM31 in detail and showed that both WH/A and WH/B motifs of MAGEA1 bind to the coiled-coil domain of TRIM31 and that MAGEA1 interaction stimulates TRIM31 ubiquitin-ligase activity. In addition, TRIM31 directly binds to NSE4, suggesting the existence of a TRIM31-MAGEA1-NSE4 complex reminiscent of the NSE1-NSE3-NSE4 trimer. These results suggest that MAGEA1 functions as a co-factor of TRIM31 ubiquitin-ligase and that the TRIM31-MAGEA1-NSE4 complex may have evolved from an ancestral NSE1-NSE3-NSE4 complex

Molecular basis for PrimPol recruitment to replication forks by RPA

DNA damage and secondary structures can stall the replication machinery. Cells possess numerous tolerance mechanisms to complete genome duplication in the presence of such impediments. In addition to translesion synthesis (TLS) polymerases, most eukaryotic cells contain a multi-functional replicative enzyme called Primase-Polymerase (PrimPol) that is capable of directly bypassing DNA damage by TLS, as well as repriming replication downstream of impediments. Here, we report that PrimPol is recruited to reprime through its interaction with RPA. Using biophysical and crystallographic approaches, we identify that PrimPol possesses two RPA-binding motifs and ascertained the key residues required for these interactions. We demonstrate that one of these motifs is critical for PrimPolʼs recruitment to stalled replication forks in vivo. In addition, biochemical analysis reveals that RPA serves to stimulate the primase activity of PrimPol. Together, these findings provide significant molecular insights into PrimPolʼs mode of recruitment to stalled forks to facilitate repriming and restart

CRISPR-Associated Primase-Polymerases are implicated in prokaryotic CRISPR-Cas adaptation

CRISPR-Cas pathways provide prokaryotes with acquired “immunity” against foreign genetic elements, including phages and plasmids. Although many of the proteins associated with CRISPR-Cas mechanisms are characterized, some requisite enzymes remain elusive. Genetic studies have implicated host DNA polymerases in some CRISPR-Cas systems but CRISPR-specific replicases have not yet been discovered. We have identified and characterised a family of CRISPR-Associated Primase-Polymerases (CAPPs) in a range of prokaryotes that are operonically associated with Cas1 and Cas2. CAPPs belong to the Primase-Polymerase (Prim-Pol) superfamily of replicases that operate in various DNA repair and replication pathways that maintain genome stability. Here, we characterise the DNA synthesis activities of bacterial CAPP homologues from Type IIIA and IIIB CRISPR-Cas systems and establish that they possess a range of replicase activities including DNA priming, polymerisation and strand-displacement. We demonstrate that CAPPs operonically-associated partners, Cas1 and Cas2, form a complex that possesses spacer integration activity. We show that CAPPs physically associate with the Cas proteins to form bespoke CRISPR-Cas complexes. Finally, we propose how CAPPs activities, in conjunction with their partners, may function to undertake key roles in CRISPR-Cas adaptation

PLK1 regulates the PrimPol damage tolerance pathway during the cell cycle

Replication stress and DNA damage stall replication forks and impede genome synthesis. During S phase, damage tolerance pathways allow lesion bypass to ensure efficient genome duplication. One such pathway is repriming, mediated by Primase-Polymerase (PrimPol) in human cells. However, the mechanisms by which PrimPol is regulated are poorly understood. Here, we demonstrate that PrimPol is phosphorylated by Polo-like kinase 1 (PLK1) at a conserved residue between PrimPol’s RPA binding motifs. This phosphorylation is differentially modified throughout the cell cycle, which prevents aberrant recruitment of PrimPol to chromatin. Phosphorylation can also be delayed and reversed in response to replication stress. The absence of PLK1-dependent regulation of PrimPol induces phenotypes including chromosome breaks, micronuclei, and decreased survival after treatment with camptothecin, olaparib, and UV-C. Together, these findings establish that deregulated repriming leads to genomic instability, highlighting the importance of regulating this damage tolerance pathway following fork stalling and throughout the cell cycle

A Branch and Bound Algorithm for the Knapsack Problem

A branch and bound algorithm for solution of the "knapsack problem," max \sum v ix i where \sum w ix i \leqq W and x i - 0, 1, is presented which can obtain either optimal or approximate solutions. Some characteristics of the algorithm are discussed and computational experience is presented. Problems involving 50 items from which approximately 25 items were loaded were solved in an average of 0.07 minutes each by a coded version of this algorithm for the IBM 7094 computer.

ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science

While the goal of OR/MS is to aid decision makers, implementation of published models occurs less frequently than one might hope. However, one area that has been significantly impacted by management science is emergency response systems. Dozens of papers on emergency service management appeared in the OR/MS literature in the 1970s alone, many of which were published in Management Science. Three of these papers won major prizes. More importantly, many of these papers led to the implementation of substantially new policies and practices, particularly in policing and firefighting. Much of this work originated in New York City, though many other cities subsequently adopted the resulting models and strategies. In this paper, we look at the context, content, and nature of the research and the factors that led to these early implementation successes. We then track the extent to which these original models are still affecting decision making in emergency response systems. We also examine the pace of development of new OR/MS models and applications in the area. Finally, we look at issues in emergency responsiveness that have emerged recently as a result of the national focus on terrorism and discuss the potential for future OR/MS modeling and application.applications, emergency services, fire, police, public sector, urban

The Lagged PSA for Estimating Peak Congestion in Multiserver Markovian Queues with Periodic Arrival Rates

We propose using a modification of the simple peak hour approximation (SPHA) for estimating peak congestion in multiserver queueing systems with exponential service times and time-varying periodic Poisson arrivals. This lagged pointwise stationary approximation (lagged PSA) is obtained by first estimating the time of the actual peak congestion by the time of peak congestion in an infinite server model and then substituting the arrival rate at this time in the corresponding stationary finite server model. We show that the lagged PSA is always more accurate than the SPHA and results in dramatically smaller errors when average service times are greater than a half an hour (based on a 24 hour period). More importantly, the lagged PSA reliably identifies proper staffing levels to meet targeted performance levels to keep congestion low.queues, nonstationarity, approximations

A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals

We study the M t /G/\infty queue where customers arrive according to a sinusoidal function \lambda t = \lambda + A sin(2\pi t/T) and the service rate is \mu . We show that the expected number of customers in the system during peak congestion can be closely approximated by (\lambda + A)/\mu for service distributions with coefficient of variation between 0 and 1. Motivated by a result derived by Eick, Massey, and Whitt that the time lag of the peak congestion from the peak of the customer arrivals is 1/2\mu for models with deterministic service times, we show that the time lag for exponential service times is closely approximated by 1/\mu . Based on a cycle length of 24 hours and regardless of the values of other system parameters, these approximations are of the order of 1% accuracy for \mu = 1, and the accuracy increases rapidly with increasing \mu .Queues, Nonstationarity, Approximations