The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

ALTER TABLE `TBL_TOWER_ANALYZER` ADD INDEX `tbl_analyzer_idx_lng_id_txt_id_dat_start` (`LNG_CASE_ID`,`TXT_SUBSCRIBER_CELL_ID`,`DAT_START`);

The optimized query:

SELECT
        TBL_TOWER_ANALYZER.LNG_TOWER_ANALYZER_ID,
        TBL_TOWER_ANALYZER.LNG_UPLOAD_ID,
        TBL_TOWER_ANALYZER.DAT_START,
        ISNULL(TBL_TOWER_ANALYZER.LNG_DURATION,
        0),
        ISNULL(TBL_TOWER_ANALYZER.INT_DIRECTION,
        0),
        ISNULL(TBL_TOWER_ANALYZER.INT_CALL_DATA_TYPE,
        0),
        TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_NUMBER,
        TBL_TOWER_ANALYZER.TXT_OTHER_PARTY_NUMBER,
        TBL_TOWER_ANALYZER.TXT_CALLING_NUMBER,
        TBL_TOWER_ANALYZER.TXT_CALLED_NUMBER,
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_IMSI,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_IMEI,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_CELL_ID,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_BTS_ADDRESS,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_LATITUDE,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_LONGITUDE,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_AZIMUTH_DEG,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_ADDRESS,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_TOC,
        ''),
        TBL_TOWER_ANALYZER.DAT_SUBSCRIBER_ACTIVATION,
        ISNULL(TBL_TOWER_ANALYZER.TXT_OTHER_PARTY_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_OTHER_PARTY_ADDRESS,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_OTHER_PARTY_TOC,
        ''),
        TBL_TOWER_ANALYZER.DAT_OTHER_PARTY_ACTIVATION,
        ISNULL(TBL_TOWER_ANALYZER.TXT_ROAMING_NETWORK_COMPANY_NAME,
        ''),
        TBL_TOWER_ANALYZER.LNG_CASE_ID,
        ISNULL(TBL_TOWER_ANALYZER.TXT_OP_SP_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_OP_COUNTRY_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_OP_CITY_NAME,
        ''),
        0,
        ISNULL(TBL_TOWER_ANALYZER.BIT_YSN_ROAMING,
        0),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUB_SP_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUB_COUNTRY_NAME,
        ''),
        ISNULL(TBL_TOWER_ANALYZER.TXT_SUB_CITY_NAME,
        '') 
    FROM
        TBL_TOWER_ANALYZER 
    WHERE
        TBL_TOWER_ANALYZER.LNG_CASE_ID = 50 
        AND TBL_TOWER_ANALYZER.TXT_SUBSCRIBER_CELL_ID IN (
            '83_34493', '83_34492', '83_34491', '56_65413', '56_65412', '56_65411', '56_65364', '56_65363', '56_65362', '56_65361', '56_65153', '56_65152', '56_65151', '56_65133', '56_65132', '56_65131', '56_53013', '56_53012', '56_53011', '56_51463', '56_51462', '56_51461', '56_51383', '56_51382', '56_51381', '56_51053', '56_51052', '56_51051', '56_50193', '56_50192', '56_50191', '56_50053', '56_50052', '56_50051', '56_46853', '56_46852', '56_46851', '56_38933', '56_38932', '56_38931', '56_33703', '56_33702', '56_33701', '56_33473', '56_33472', '56_33471', '56_32443', '56_32442', '56_32441', '56_26113', '56_26112', '56_26111', '56_17143', '56_17142', '56_17141', '56_16803', '56_16802', '56_16801', '56_16193', '56_16192', '56_16191', '56_16083', '56_16082', '56_16081', '56_15533', '56_15532', '56_15531', '56_10284', '56_10283', '56_10282', '56_10281', '29_51483', '29_51482', '29_51481', '29_51423', '29_51422', '29_51421', '29_50943', '29_50942', '29_50941', '29_50913', '29_50912', '29_50911', '29_50383', '29_50382', '29_50381', '29_50373', '29_50372', '29_50371', '29_50343', '29_50342', '29_50341', '29_50333', '29_50332', '29_50331', '29_50323', '29_50322', '29_50321', '29_50313', '29_50312', '29_50311', '29_50303', '29_50302', '29_50301', '29_50293', '29_50292', '29_50291', '29_50283', '29_50282', '29_50281', '29_50263', '29_50262', '29_50261', '29_50253', '29_50252', '29_50251', '29_50243', '29_50242', '29_50241', '29_50234', '29_50233', '29_50232', '29_50231', '29_50223', '29_50222', '29_50221', '29_50203', '29_50202', '29_50201', '29_43603', '29_43602', '29_43601', '29_43483', '29_43482', '29_43481', '29_43103', '29_43102', '29_43101', '29_37203', '29_37202', '29_37201', '29_37113', '29_37112', '29_37111', '29_36974', '29_36973', '29_36972', '29_36971', '29_36964', '29_36963', '29_36962', '29_36961', '29_34993', '29_34992', '29_34991', '29_34983', '29_34982', '29_34981', '29_34723', '29_34722', '29_34721', '29_34483', '29_34482', '29_34481', '29_33863', '29_33862', '29_33861', '29_33353', '29_33352', '29_33351', '29_32563', '29_32562', '29_32561', '29_31633', '29_31632', '29_31631', '29_28683', '29_28682', '29_28681', '29_27933', '29_27932', '29_27931', '29_16933', '29_16932', '29_16931', '29_16773', '29_16772', '29_16771', '29_13013', '29_13012', '29_13011', '100_57213', '100_57212', '100_57211', '100_51103', '100_51102', '100_51101', '100_50986', '100_50985', '100_50984', '100_50983', '100_50982', '100_50981', '100_50216', '100_50214', '100_50213', '100_50212', '100_50211', '100_26223', '100_26222', '100_26221', '100_19823', '100_19822', '100_19821', '100_18363', '100_18362', '100_18361'
        ) 
        AND TBL_TOWER_ANALYZER.DAT_START BETWEEN '2013-05-24 01:00:00' AND '2013-05-24 12:59:59'