A multiserver queueing system with infinite and finite buffers, two types of customers, and two types of servers as a model of a call center with a call-back for lost customers is investigated. Type 1 customers arrive to the system according to a Markovian arrival process. All rejected type 1 customers become type 2 customers. Typer,r=1,2, servers serve typercustomers if there are any in the system and serve typer′,r′=1,2,  r′≠r,customers if there are no typercustomers in the system. The service times of different types of customers have an exponential distribution with different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution of type 2 customers is derived. The problem of optimal choice of the number of each type servers is solved numerically.

Many registration schemes have been proposed to reduce the signaling cost required for user’s mobility management in wireless communication networks. Various results on mobility management schemes to minimize the total signaling cost have been reported. The objective of this study was to analyze a registration scheme that could deal with mobility prediction and corresponding flexible tracking area list (TAL) forming. In this scheme, based on mobility prediction and corresponding TAL forms, a new TAL was constructed such that the registration cost could be minimized. In addition, a semi-Markov process model was newly presented for the registration scheme considering mobility prediction and corresponding flexible TAL forming for two different environments: urban and rural. Simulation studies were also performed to validate the accuracy of the semi-Markov process model. Numerical results showed that analytical and simulation results were very close (average relative error of 1.4%). The registration cost decreased as the moving probability (q) to the predicted direction increased. The performance of the proposed scheme was superior to distance-based registration (DBR) or TAL-based scheme especially when q was high. When call-to-mobility ratio was less than or equal to 1 corresponding to current small cell configurations, the proposed scheme outperformed the DBR or TAL-based scheme.

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In this study, we consider zone-based registration (ZBR). In the ZBR, when a mobile station (MS) enters a new location area (LA), it registers its location. Among various types of ZBR, we focus on two zone-based registration with outgoing call (TZRC) that is an improved version of the two zone-based registration (TZR). In the TZR, an MS can store two LAs that it registers recently not to register when it crosses two LAs stored already. In general, TZR has better performance than single zone-based registration (SZR). However, since the TZR may increase paging cost, TZRC was proposed to decrease paging cost. Mathematical analysis is performed to obtain the exact performance of SZR, TZR, TZRC. From the numerical results for various circumstances, it is shown that TZRC outperforms TZR and SZR in most cases.